Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Wind Tunnel Investigations of an Inclined

Stay Cable with a Helical Fillet

PUBLICATION NO. FHWA-HRT-14-070 SEPTEMBER 2014
FOREWORD

Cable-stayed bridges have become the form of choice over the past several decades for bridges 

in the medium-to-long-span range. In some cases, serviceability problems involving large 

amplitude vibrations of stay cables under certain wind and wind-rain conditions have been 

observed. This study was conducted in response to State transportation departments’ requests to 

develop improved design guidance for mitigation of excessive cable vibrations on cable-stayed 

bridges. The study included wind tunnel testing of a full-scale cable model to evaluate the 

influence of damping, turbulence, and aerodynamic surface treatment on cable stability. The 

results of this study will be made available to the Post-Tensioning Institute’s DC-45 CableStayed Bridge Committee for consideration during their periodic updates of the Guide 

Specification, Recommendations for Stay Cable Design, Testing, and Installation.

(1)

This report will be of interest to bridge engineers, wind engineers, and consultants involved in 

the design of cable-stayed bridges. It is the third in a series of reports addressing the subject of 

aerodynamic stability of bridge stay cables that will be published in the coming months. 

Jorge E. Pagán-Ortiz

Director, Office of Infrastructure

Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

in the interest of information exchange. The U.S. Government assumes no liability for the use 

of the information contained in this document. This report does not constitute a standard, 

specification, or regulation.

The U.S. Government does not endorse products or manufacturers. Trademarks or 

manufacturers’ names appear in this report only because they are considered essential to the 

objective of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement.
TECHNICAL DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-14-070

2. Government Accession No. 3. Recipient’s Catalog No.

4. Title and Subtitle

Wind Tunnel Investigations of an Inclined Stay Cable with a Helical Fillet

5. Report Date

September 2014

6. Performing Organization Code

7. Author(s)

Guy L. Larose and Annick D’Auteuil

8. Performing Organization Report No.

LTR-AL-2011-0093

9. Performing Organization Name and Address

National Research Council of Canada

Institute for Aerospace Research

1200 Montreal Road

Ottawa, Ontario Canada K1A OR6

Genex Systems, LLC

2 Eaton Street, Suite 603

Hampton, VA 23669

10. Work Unit No. (TRAIS)

11. Contract or Grant No.

DTFH61-07-D-00034

12. Sponsoring Agency Name and Address

Office of Infrastructure R&D

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

13. Type of Report and Period Covered

Laboratory Report

March 2011–March 2012

14. Sponsoring Agency Code

HRDI-50

15. Supplementary Notes

The Contracting Officer’s Technical Representative (COTR) was Harold R. Bosch, (HRDI-50).

16. Abstract

Cable-stayed bridges have been recognized as the most efficient and cost effective structural form for medium-to-longspan bridges over the past several decades. With their widespread use, cases of serviceability problems associated 

with large amplitude vibration of stay cables have been reported. Stay cables are laterally flexible structural members 

with very low inherent damping and thus are highly susceptible to environmental conditions such as wind and 

rain/wind combination. 

Recognition of these problems has led to the incorporation of different types of mitigation measures on many cablestayed bridges around the world. These measures include surface modifications, cable crossties, and external dampers. 

Modification of cable surfaces has been widely accepted as a means to mitigate rain/wind vibrations. Recent studies 

have firmly established the formation of a water rivulet along the upper side of the stay and its interaction with wind 

flow as the main cause of rain/wind vibrations. Appropriate modifications to exterior cable surfaces effectively disrupts 

the formation of a water rivulet.

The objective of this study is to supplement the existing knowledge base on some of the outstanding issues of stay 

cable vibrations and to develop technical recommendations that may be incorporated into design guidelines. 

Specifically, this project focused on the wind-cable interaction, with particular interest in details of the air flow and 

flow field close to the cable as well as forces on the cable surface. A helical fillet was attached to an existing cable 

model to evaluate the influence of this common mitigation feature on dynamic behavior. The cable inclination angle 

was varied during testing to represent field orientations, and the model was rotated on its longitudinal axis to assess the 

influence of high-density polyethylene roundness. Tests were conducted at various levels of damping, with and without 

the fillet, and in turbulent as well as smooth flow conditions.

17. Key Words

Cable-stayed bridges, Cables, Vibrations, Wind, Rain, 

Wind tunnel testing, Wind turbulence, Galloping, Vortex 

shedding, Aerodynamic surface treatment, Helical fillet

18. Distribution Statement

No restrictions. This document is available to the public 

through the National Technical Information Service, 

Springfield, VA 22161.

http://www.ntis.gov

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

222

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius o

C 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380. 

(Revised March 2003)

ii
TABLE OF CONTENTS

EXECUTIVE SUMMARY .......................................................................................................... 1

CHAPTER 1: INTRODUCTION................................................................................................ 3

CHAPTER 2: EXPERIMENTAL CONDITIONS .................................................................... 5

PROTOTYPE STAY CABLES............................................................................................. 5

MODEL PROPERTIES......................................................................................................... 8

SUSPENSION SYSTEM...................................................................................................... 10

FLOW CONDITIONS.......................................................................................................... 15

Smooth Flow..................................................................................................................... 15

Turbulent Flow.................................................................................................................. 17

CHAPTER 3: EXPERIMENTAL PROCEDURES AND ANALYSIS.................................. 23

TEST PROGRAM ................................................................................................................ 23

INSTRUMENTATION ........................................................................................................ 25

TEST PROCEDURES.......................................................................................................... 27

DATA ANALYSIS AND REPORTING............................................................................. 32

CHAPTER 4: RESULTS AND DISCUSSION OF EXPERIMENTS ................................... 33

GENERAL............................................................................................................................. 33

INFLUENCE OF THE ATTITUDE OF THE CABLE TO THE MAIN WIND 

FLOW .................................................................................................................................... 35

Influence of the Cable Rotation ........................................................................................ 35

Influence of Cable-Wind Angle Plane.............................................................................. 36

Influence of Cable Inclination .......................................................................................... 38

INFLUENCE OF STRUCTURAL DAMPING ................................................................. 39

INFLUENCE OF TURBULENCE...................................................................................... 43

INFLUENCE OF THE HELICAL FILLET...................................................................... 46

INFLUENCE OF MOTION ON THE MEAN AERODYNAMIC FORCE 

COEFFICIENTS................................................................................................................... 48

INFLUENCE OF THE END CONDITIONS AT THE TOP OF THE CABLE 

MODEL ................................................................................................................................. 50

RELATIONSHIP BETWEEN THE SURFACE PRESSURES AND THE WAKE 

SIGNATURE......................................................................................................................... 51

GENERAL CHARACTERISTICS OF MEAN FORCE COEFFICIENTS WITH 

REYNOLDS NUMBER........................................................................................................ 52

REPEATABILITY OF THE TESTS.................................................................................. 58

MECHANISMS CAUSING THE VIBRATIONS ............................................................. 62

CHAPTER 5: CONCLUSIONS ................................................................................................ 65

APPENDIX A. DETAILED LIST OF RUNS AND EXPERIMENTAL CONDITIONS .... 67

APPENDIX B. SUMMARY OF RESULTS............................................................................. 75

ACKNOWLEDGEMENTS ..................................................................................................... 203

REFERENCES.......................................................................................................................... 205

iii
LIST OF FIGURES

Figure 1. Photo. Modern stay cables with HDPE tube cover on the Millau Viaduct ..................... 5

Figure 2. Photo. Modern stay cables with HDPE tube cover on the Clark Bridge......................... 6

Figure 3. Photo. Pitch and helix angle ............................................................................................ 8

Figure 4. Graph. Variations of the cable model diameter with azimuth at four span-wise 

locations.......................................................................................................................................... 9

Figure 5. Photo. Close-up view of double helical right-handed fillet........................................... 10

Figure 6. Photo. Overview of double helical right-handed fillet .................................................. 10

Figure 7. Photo. Lower rig with spring rotation at 0 degrees....................................................... 11

Figure 8. Photo. Upper rig with spring rotation at 45 degrees...................................................... 11

Figure 9. Photo. Cable model at an inclination of 60 degrees from outside the test section 

of the 3-by-6-m Propulsion and Icing Wind Tunnel..................................................................... 12

Figure 10. Photo. Cable model at an inclination of 60 degrees from inside the test section 

of the 3-by-6-m Propulsion and Icing Wind Tunnel..................................................................... 13

Figure 11. Photo. Turntable that allowed rotation of the cable model on its axis........................ 13

Figure 12. Photo. Top of the open interface between the cable model and the roof of the 

wind tunnel.................................................................................................................................... 15

Figure 13. Photo. Underside of the sealed interface between the cable model and the roof 

of the wind tunnel ......................................................................................................................... 15

Figure 14. Photo. Downstream view of the test section during dynamic pressure calibration 

prior to the installation of the cable model ................................................................................... 16

Figure 15. Graph. Variations of Iu with wind speed measured at the entrance of the test 

section for different external conditions for the smooth flow case............................................... 17

Figure 16. Photo. Grid of ladders used to generate the turbulent flow field for position 1.......... 18

Figure 17. Photo. Grid of ladders used to generate the turbulent flow field for position 2.......... 19

Figure 18. Photo. TFI Cobra Probe attached to the cable model to measure the turbulence 

level behind the grid of ladders..................................................................................................... 19

Figure 19. Graph. Variations of the normalized spectral densities of the wind velocity 

fluctuations with frequencies for the smooth and turbulent flow cases........................................ 20

Figure 20. Graph. Vertical and lateral profiles of the intensity of turbulence for the three 

wind components for the turbulent flow for position 2 ................................................................ 20

Figure 21. Equation. Model inclination ........................................................................................ 25

Figure 22. Equation. Spring rotation............................................................................................. 25

Figure 23. Illustration. Sketch of the pressure tap arrangement ................................................... 27

Figure 24. Photo. Model inspection in the test section................................................................. 28

Figure 25. Graph. Growth of the cable model vibration as a function of time inclined at

60 degrees and rotated at -88 degrees........................................................................................... 29

Figure 26. Graph. Growth of the cable model vibration as a function of time inclined at

60 degrees and rotated at -90 degrees........................................................................................... 30

Figure 27. Graph. Example of decay trace for the sway mode of vibration and corresponding 

variation of damping with amplitude of vibrations....................................................................... 30

Figure 28. Photo. Procedures followed to set the azimuth angle of the cable model ................... 31

Figure 29. Graph. Amplitude of motion in sway for four different rotations of the cable along 

its main axis for the cable inclined at 60 degrees with helical fillet and in smooth flow............. 35

iv
Figure 30. Graph. Amplitude of motion in sway for three different spring plane rotations 

for the cable inclined at 60 degrees with helical fillet and in smooth flow .................................. 37

Figure 31. Photo. Cable model at 45-degree inclination and 0-degree spring rotation with 

smooth flow .................................................................................................................................. 38

Figure 32. Graph. Mean force coefficients calculated from the integration of surface pressure 

measurements for the cable inclined at 60 and 45 degrees and rotated at -90 degrees along its 

main axis in smooth flow and with a helical fillet........................................................................ 39

Figure 33. Photo. Elastic bands used to increase the structural damping of the suspension 

system ........................................................................................................................................... 40

Figure 34. Equation. Scrunton number......................................................................................... 40

Figure 35. Photo. Viscoelastic washer used to increase the structural damping of the 

suspension system......................................................................................................................... 41

Figure 36. Graph. Structural damping level as a function of amplitude of motion of the cable 

for the sway mode......................................................................................................................... 41

Figure 37. Graph. Structural damping level as a function of amplitude of motion of the cable 

for the heave mode........................................................................................................................ 42

Figure 38. Graph. Response of the cable model as a function of wind speed or Reynolds 

number for three damping levels as measured by lasers, accelerometers, and surface pressures 

for different levels of damping ..................................................................................................... 43

Figure 39. Photo. Cable model at 60-degree inclination and 0-degree spring rotation in 

turbulent flow................................................................................................................................ 44

Figure 40. Graph. Amplitude of motion in sway and end-to-end sway at cable rotation of

-90 degrees and inclined at 60 degrees with a helical fillet in smooth and turbulent flow........... 45

Figure 41. Graph. Mean force coefficients at cable rotation of -90 degrees and inclined at

60 degrees with a helical fillet in smooth and turbulent flow....................................................... 45

Figure 42. Graph. Amplitude of motion in sway and end-to-end sway at cable rotation of

-90 degrees and inclined at 60 degrees without a helical fillet in smooth and turbulent flow...... 46

Figure 43. Graph. Mean force coefficients at cable rotation of -90 degrees and inclined at

60 degrees without a helical fillet in smooth and turbulent flow.................................................. 46

Figure 44. Graph. Amplitude of motion in sway and end-to-end sway for cable rotated at

-90 and 0 degrees and inclined at 60 degrees in smooth flow with and without a helical fillet ... 47

Figure 45. Graph. Mean force coefficients for cable rotated at 0 degrees and inclined at 

60 degrees in smooth flow with and without helical fillet............................................................ 47

Figure 46. Illustration. Distribution of surface pressure coefficient for the four rings with 

the cable in a static position (run 81)............................................................................................ 48

Figure 47. Illustration. Distribution of surface pressure coefficient for the four rings with 

the cable in motion (run 122)........................................................................................................ 49

Figure 48. Graph. Mean force coefficients as a function of cable rotation for the static cable 

and as a function of wind speed for cable in motion .................................................................... 50

Figure 49. Photo. TFI Cobra Probe placed in the wake of the cable model directly behind 

ring 3 of pressure taps................................................................................................................... 51

Figure 50. Graph. Spectrum of the longitudinal flow velocity fluctuations located in the 

wake of the model and spectrum of the surface pressure signal of port 30 on ring 3 with a 

wind speed of 24 m/s .................................................................................................................... 52

Figure 51. Graph. Variations of Cx and Cy with wind speed for 17 cable rotations with 

cable inclined at 60 degrees in smooth flow and with the helical fillet........................................ 54

v
Figure 52. Graph. Variations of Cx and Cy with wind speed for five cable rotations with 

cable inclined at 60 degrees in turbulent flow and with the helical fillet ..................................... 55

Figure 53. Graph. Variations of Cx and Cy with wind speed for six cable rotations with 

cable inclined at 60 degrees in turbulent flow and without the helical fillet ................................ 56

Figure 54. Graph. Variations of Cx and Cy with wind speed for seven cable rotations with 

cable inclined at 60 degrees in smooth flow and without the helical fillet................................... 57

Figure 55. Graph. Variations of Cx and Cy with wind speed for five cable rotations with 

cable inclined at 45 degrees in smooth flow and with the helical fillet........................................ 58

Figure 56. Graph. Mean Cx and Cy calculated from the integration of surface pressure 

measurements for two runs with cable inclined at 60 degrees and rotated at -90 degrees in 

smooth flow and with helical fillet ............................................................................................... 60

Figure 57. Graph. Response of the cable for two consecutive runs for the cable inclined at 

60 degrees and rotated at 2 degrees in smooth flow and without the helical fillet....................... 61

Figure 58. Graph. Amplitude of motion in sway for four consecutive runs for the cable 

inclined at 60 degrees and rotated at -88 degrees without the helical fillet and in smooth 

flow ............................................................................................................................................... 62

Figure 59. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 27 ................................... 75

Figure 60. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 27 ............................................................................................................................................ 76

Figure 61. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 28............................... 77

Figure 62. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 28 ............................................................................................................................................ 78

Figure 63. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 32............................................................................................................. 79

Figure 64. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 35............................................................................................................. 80

Figure 65. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 37............................................................................................................. 81

Figure 66. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 39............................................................................................................. 82

Figure 67. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 41............................................................................................................. 83

Figure 68. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 44 ................................... 84

Figure 69. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 44 ............................................................................................................................................ 85

vi
Figure 70. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 46 ................................... 86

Figure 71. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 46 ............................................................................................................................................ 87

Figure 72. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 49 ................................... 88

Figure 73. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 49 ............................................................................................................................................ 89

Figure 74. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 52 ................................... 90

Figure 75. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 52 ............................................................................................................................................ 91

Figure 76. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 56 ................................... 92

Figure 77. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 56 ............................................................................................................................................ 93

Figure 78. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 60 ................................... 94

Figure 79. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 60 ............................................................................................................................................ 95

Figure 80. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 63 ................................... 96

Figure 81. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 63 ............................................................................................................................................ 97

Figure 82. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 66 ................................... 98

Figure 83. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 66 ............................................................................................................................................ 99

Figure 84. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 67 ................................. 100

Figure 85. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 67 .......................................................................................................................................... 101

Figure 86. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 69 ................................. 102

Figure 87. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 69 .......................................................................................................................................... 103

vii
Figure 88. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 71 ................................. 104

Figure 89. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 71 .......................................................................................................................................... 105

Figure 90. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 73 ................................. 106

Figure 91. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 73 .......................................................................................................................................... 107

Figure 92. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 75 ................................. 108

Figure 93. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 75 .......................................................................................................................................... 109

Figure 94. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 81........................................................................................................... 110

Figure 95. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 85........................................................................................................... 111

Figure 96. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 88........................................................................................................... 112

Figure 97. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 90........................................................................................................... 113

Figure 98. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 92........................................................................................................... 114

Figure 99. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 94........................................................................................................... 115

Figure 100. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 101 ............................... 116

Figure 101. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 101 ........................................................................................................................................ 117

Figure 102. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 108 ............................... 118

Figure 103. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 108 ........................................................................................................................................ 119

Figure 104. Graph. Response of the cable as a function of wind speed or Reynolds number as 

measured by the lasers, accelerometers, and surface pressures for run 118 ............................... 120

viii
Figure 105. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 118 ........................................................................................................................................ 121

Figure 106. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 122........................... 122

Figure 107. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 122 ........................................................................................................................................ 123

Figure 108. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 123........................... 124

Figure 109. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 123 ........................................................................................................................................ 125

Figure 110. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 125........................... 126

Figure 111. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 125 ........................................................................................................................................ 127

Figure 112. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 131........................... 128

Figure 113. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 131 ........................................................................................................................................ 129

Figure 114. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 136........................... 130

Figure 115. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 136 ........................................................................................................................................ 131

Figure 116. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 137........................... 132

Figure 117. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 137 ........................................................................................................................................ 133

Figure 118. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 140........................... 134

Figure 119. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 140 ........................................................................................................................................ 135

Figure 120. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 142........................... 136

Figure 121. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 142 ........................................................................................................................................ 137

Figure 122. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 144........................... 138

ix
Figure 123. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 144 ........................................................................................................................................ 139

Figure 124. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 149........................... 140

Figure 125. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 149 ........................................................................................................................................ 141

Figure 126. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 152........................... 142

Figure 127. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 152 ........................................................................................................................................ 143

Figure 128. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 155........................... 144

Figure 129. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 155 ........................................................................................................................................ 145

Figure 130. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 159........................... 146

Figure 131. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 159 ........................................................................................................................................ 147

Figure 132. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 163........................... 148

Figure 133. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 163 ........................................................................................................................................ 149

Figure 134. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 167........................... 150

Figure 135. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 167 ........................................................................................................................................ 151

Figure 136. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 176........................... 152

Figure 137. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 176 ........................................................................................................................................ 153

Figure 138. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 178........................... 154

Figure 139. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 178 ........................................................................................................................................ 155

Figure 140. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 197........................... 156

x
Figure 141. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 197 ........................................................................................................................................ 157

Figure 142. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 199........................... 158

Figure 143. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 199 ........................................................................................................................................ 159

Figure 144. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 203........................... 160

Figure 145. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 203 ........................................................................................................................................ 161

Figure 146. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 206........................... 162

Figure 147. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 206 ........................................................................................................................................ 163

Figure 148. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 208........................... 164

Figure 149. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 208 ........................................................................................................................................ 165

Figure 150. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 211........................... 166

Figure 151. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 211 ........................................................................................................................................ 167

Figure 152. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 214........................... 168

Figure 153. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 214 ........................................................................................................................................ 169

Figure 154. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 216........................... 170

Figure 155. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 216 ........................................................................................................................................ 171

Figure 156. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 219........................... 172

Figure 157. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 219 ........................................................................................................................................ 173

Figure 158. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 222........................... 174

xi
Figure 159. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 222 ........................................................................................................................................ 175

Figure 160. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 225........................... 176

Figure 161. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 225 ........................................................................................................................................ 177

Figure 162. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 226........................... 178

Figure 163. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 226 ........................................................................................................................................ 179

Figure 164. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 230........................... 180

Figure 165. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 230 ........................................................................................................................................ 181

Figure 166. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 234........................... 182

Figure 167. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 234 ........................................................................................................................................ 183

Figure 168. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 237........................... 184

Figure 169. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 237 ........................................................................................................................................ 185

Figure 170. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 239........................... 186

Figure 171. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 239 ........................................................................................................................................ 187

Figure 172. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 244........................... 188

Figure 173. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 244 ........................................................................................................................................ 189

Figure 174. Graph. Intensity of turbulence measured at the entrance of the test section and 

Cx and Cy calculated from surface pressure measurements as a function of Reynolds number

and wind speed for run 248......................................................................................................... 190

Figure 175. Graph. Intensity of turbulence measured at the entrance of the test section 

and Cx and Cy calculated from surface pressure measurements as a function of Reynolds 

number and wind speed for run 250 ........................................................................................... 191

Figure 176. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 253........................... 192

xii
Figure 177. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 253 ........................................................................................................................................ 193

Figure 178. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 255........................... 194

Figure 179. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 255 ........................................................................................................................................ 195

Figure 180. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 257........................... 196

Figure 181. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 257 ........................................................................................................................................ 197

Figure 182. Graph. Response of the cable as a function of wind speed or Reynolds number

as measured by the lasers, accelerometers, and surface pressures for run 260........................... 198

Figure 183. Graph. Mean displacement and peak factor from the laser, motion path at one 

wind speed, and intensity of turbulence measured at the entrance of the test section for 

run 260 ........................................................................................................................................ 199

Figure 184. Graph. Damping traces and level for the sway and heave modes for the low 

damping level case...................................................................................................................... 200

Figure 185. Graph. Damping traces and level for the sway and heave modes for the 

medium damping case................................................................................................................. 201

Figure 186. Graph. Damping traces and level for the sway and heave modes for the high 

damping level case...................................................................................................................... 202

xiii
LIST OF TABLES

Table 1. Typical prototype helical fillet geometries (all double helix)........................................... 7

Table 2. Number of active coils per spring................................................................................... 14

Table 3. Cable length or distance for instrumentation at both extremities of the cable ............... 14

Table 4. Summary of test program for phases I and II ................................................................. 24

Table 5. Relationship between model wind-angle planes and field conditions............................ 25

Table 6. Description of all the runs completed during the wind tunnel test ................................. 67

xiv
LIST OF SYMBOLS

Symbols

Cd Drag coefficient.

Cx Along-wind force coefficient.

Cy Across-wind force coefficient

d, D Cable diameter.

f Frequency.

I Turbulence intensity.

L Wind exposed length of cable model.

x

L Integral length scale of turbulence.

m Mass per unit exposed length of cable model.

q Dynamic pressure.

Re Reynolds number.

Sc Scruton number.

U Mean wind speed.

U/ f B Reduced velocity.

Spring rotation.

Flow yaw angle.

Damping ratio as a fraction of critical.

θ Stay cable inclination.

Air viscosity.

ρ Air density.

Model inclination.

Subscripts

h Heave, along-wind.

s Sway, across-wind.

u,v,w Longitudinal, lateral, and vertical components of the flow fluctuations.

α

β

ζ

μ

φ

xv

EXECUTIVE SUMMARY

Experiments on a 1:1 scale sectional model of a stay cable were conducted in the 3-by-6-m 

Propulsion and Icing Wind Tunnel at the Institute for Aerospace Research, National Research 

Council Canada (NRC-IAR). The purpose of the experiments was to study the effect of adding a 

helical fillet to the surface of a stay cable and monitor the response of the cable during windinduced excitation.

The experiments were carried out on a 6.7-m-long sectional model with a diameter of 0.162 m 

composed of a central steel core covered with a high-density polyethylene (HDPE) tube obtained 

from a bridge construction site. A double parallel helical fillet with a rectangular cross section of 

2.3 by 2.4 mm and a right-handed helix angle of 45 degrees was glued to the surface of the 

model. The geometry of the helical fillet was selected to represent what is currently used on stay 

cables of long-span cable-stayed bridges to mitigate rain/wind-induced oscillations.

The sectional model was mounted in an eight-spring suspension rig allowing along-wind and 

across-wind vibrations of the model at a frequency of 1.4 Hz in both directions. The total sprung 

mass was 406 kg, and the inherent structural damping of the suspension rig was low, between 

0.07 and 0.15 percent of critical damping for vibration amplitudes observed during the tests. 

Simultaneous measurements of fluctuating surface pressures on the circumference of the model 

and response at its extremities were carried out for wind speeds ranging from 4 to 36 m/s 

covering the entire critical number regime and beyond (43,000 < Re < 391,000), where Re

represents Reynolds number.

The wind-tunnel investigation included experiments with the cable model at 60- and 45-degree 

inclinations in smooth flow with the helical fillet, at a 60-degree inclination in turbulent flow 

with and without the helical fillet, and at a 60-degree inclination in smooth flow without the

helical fillet. The tests were conducted for several rotations of the cable model on its 

longitudinal axis.

The experiments revealed that a stay cable with a helical fillet inclined at 60 degrees to the flow 

can experience wind-induced vibrations with large amplitudes in smooth or turbulent flow for a 

low level of structural damping. The oscillations observed appeared to be self-limited in 

amplitude and could be mitigated with an increase of structural damping. The cable model with 

the helical fillet experienced a drag crisis almost as pronounced as for the smooth cable. The 

experiments also revealed that the aerodynamic forces at the source of the vibrations were highly 

sensitive to a rotation of the cable model on its axis. Measurements of the external diameter of 

the smooth cable model have shown a maximum eccentricity equivalent to 1 percent of the mean 

diameter, which appeared to be sufficient to influence the aerodynamics of the cable model, even 

with the helical fillet in place.

1

CHAPTER 1: INTRODUCTION

In response to concerns expressed in the wind engineering community with regards to the 

aerodynamics of inclined stay cables with helical fillets, NRC-IAR, in collaboration with the 

University of Bristol and the University of Stavanger, was mandated to conduct an experimental 

study in its 3-by-6-m Propulsion and Icing Wind Tunnel. This project was initiated by the 

Federal Highway Administration (FHWA), which has undertaken the task to fill the knowledge 

gap on aerodynamics of stay cables with helical fillets. The main objective of the investigation 

was to define the sensitivity of stay cables with helical fillets (such as those commonly used on 

cable-stayed bridges in the United States and Europe) to galloping. For this purpose, a small 

helical fillet was affixed to an existing stay cable model composed of a steel core covered with a 

HDPE tube, typical of actual bridge stay cables. The aeroelastic stability of the cable as well as 

the nature of underlying aerodynamic forces were investigated.

The investigation was divided in two phases. In phase I, the aerodynamic stability of a cable 

with helical fillets was studied with a spring-supported cable model in smooth flow for a 

cable inclined at 60 degrees from the horizontal. The dynamic response of the model 

and the cross-sectional wind-induced surface pressures were monitored as a function of 

Reynolds number.

In phase II, different cable orientations were studied (45 and 60 degrees). For the cases where 

important cable vibrations were observed in smooth flow, tests in turbulent flow for conditions 

representative of field conditions were carried out.

This report documents the work undertaken by NRC-IAR and presents the results of the 

investigation. The approach adopted was to carry out the test in a 3-by-6-m wind tunnel on a 

6.7-m-long sectional model built at a geometrical scale of 1:1 and free to respond on an eightspring suspension system. The tests took place from May 2, 2011, to June 24, 2011. 

The main findings of the investigation for both rounds of tests are presented in this report. The 

documentation of the tests also includes video recordings, still images, and all the experimental 

data in electronic form.

3

CHAPTER 2: EXPERIMENTAL CONDITIONS

PROTOTYPE STAY CABLES

Over the last 20 years, structural engineers and architects have proposed the use of cable-stayed 

bridges for increasingly diverse situations. Either for long main spans where only suspension 

bridges would have been traditionally considered or wide roadways with medium spans where 

cantilever or arch bridges would have been selected, cable-stayed bridges are now being built as 

the more economical and practical solution. This has promoted the development of innovative 

structural design and fabrication techniques. For example, the majority of the modern cablestayed bridges now use stay cables that are fabricated directly on the construction site as opposed 

to being pre-fabricated in a factory and shipped to the site in large coils, providing substantial 

cost and time savings.

Typical in-situ fabricated stay cables are each made of a bundle of parallel steel cables that are 

fed through an HDPE tube one by one and are anchored to the towers and deck at a prescribed 

tension. Each cable is made of five to seven steel strands and is covered by a polyethylene 

sheath. A 16-cm external diameter stay cable would be made of approximately 40 to 55 steel 

cables and would have a mass per unit length of 60 to 80 kg/m. Approximately 50 to 60 percent

of the surface area of the stay is steel, and the other 40 to 50 percent is polyethylene, air, grease, 

wax, or concrete grout. Figure 1 and figure 2 show stay cables of the Millau Viaduct in France 

and the Clark Bridge that spans from Alton, IL, to West Alton MO, respectively.

Figure 1. Photo. Modern stay cables with HDPE tube cover on the Millau Viaduct.

5
Figure 2. Photo. Modern stay cables with HDPE tube cover on the Clark Bridge.

The HDPE tube serves three main purposes: (1) aerodynamic drag reduction, (2) corrosion 

protection, and (3) aesthetics. However, it has some drawbacks, in particular when it comes to 

the effects of wind. Stay cables generally have low structural damping (≈ 0.1 to 0.2 percent of 

critical damping) and are exposed to wind and are thus prone to wind-induced vibrations. The 

HPDE tube helps by reducing the drag coefficient of the stays, therefore reducing vibrations due 

to buffeting from turbulence. However, the smooth surface of the tube combined with light rain 

and light winds can translate to severe rain/wind-induced vibrations of the stay cables. Also, the 

smooth surface of the tube in combination with its attitude (inclination and yaw angles) to the 

wind can induce undesirable dry-inclined cable galloping for a specific range of mean wind 

speeds corresponding to the critical Reynolds number regime.

To mitigate the increased sensitivity to wind-induced vibrations of the stay cable covered with a 

smooth HDPE tube, three approaches are being used:

• Increase the structural damping of the stays.

• Alter the surface of the HDPE tubes to prevent the formation of water rivulets and 

prevent rain/wind-induced vibrations.

• Install ropes or crossties between the stays.

Since the construction of the Pont de Normandie in France in the early 1990s, the majority of 

cable-stayed bridges built in Europe and North America have stay cables fitted with a helical 

fillet to prevent rain/wind vibrations. This countermeasure has proven to be highly effective 

against this phenomenon, in particular when combined with an increase of structural damping. 

6
Wind tunnel tests have been conducted to verify that the helical fillet worked.

(2,3) However, no

official design guidelines or specifications exist on what the geometry of the helical fillet should 

be for it to be effective. The industry has adopted what experience has shown as a viable solution 

based on its first use for Pont de Normandie, and nowadays, stay cable manufacturers are each 

proposing their own solutions. Table 1 presents a short list of helical fillet geometry that has

been installed on bridges. The pitch and helix angle of the helical fillet are defined in figure 3.

For this study, a double, parallel, and right-handed helical fillet was used.

Table 1. Typical prototype helical fillet geometries (all double helix).

Bridge and 

Location

Cable 

Diameter

(mm)

Pitch

(mm)

Helix 

Angle

(degrees)

Pitch to 

Diameter 

Ratio

Helical Fillet

(mm)

Description

Helical 

Fillet

Normandie; 

France

170 600 41.7 3.5 1.3 diameter Round

Oresund; 

Sweden to 

Denmark

250 550 55.0 2.2 2.1 high × 3.0 wide Rectangular

Charles River; 

Boston, MA

178 610 42.5 3.4 1.5 high × 3.3 wide Rectangular

Generic 1 200 600 46.3 3.0 2.0 diameter Round

Generic 2 160 490 45.7 3.1 4.0 diameter Round

Generic 3 200 620 45.4 3.1 2.0 diameter ×

4.0 wide

Round

Generic 4 200 630 45.0 3.1 2.0 diameter ×

4.0 wide

Round

Present study 162 520 44.4 3.2 2.3 high × 2.4 wide Rectangular

Note: Generic refers to HDPE pipe specimens with helical fillet.

7
Figure 3. Photo. Pitch and helix angle. 

Without official specifications for the helical fillet geometry, it is understandable that the 

aerodynamics of the stay cable with a helical fillet is not generally well defined. It is hard to find 

in literature the mean force coefficients of stay cables with helical fillets and, in particular, the 

across-wind coefficients. The rule of thumb is that the helical fillet increases the drag coefficient 

of the stay cables to around 0.7 to 0.8. For stay cables inclined and yawed to the wind with a 

helical fillet (i.e., for the majority of stay cables built in the last 15 years), the aerodynamic force 

coefficients are not available.

Whether such alteration to the smooth HDPE tube covering the stays could cause inclined cable 

galloping is not known, and to the authors’ knowledge, this issue has not been addressed. The 

purpose of the present study is to fill this gap.

MODEL PROPERTIES

The cable model used for two previous 1:1 scale studies in 2001 and 2008 at NRC-IAR in 

the same wind tunnel facility was reused for the present study. (See references 4–7.) No 

modifications of the model itself were necessary with the exception of a thorough cleaning of the

surface to make it as uniform as possible, a verification of each of the surface pressure taps and 

pneumatic tubing installed for the 2008 measurement campaign and the installation of removable 

helical fillets.

The model was composed of a rigid steel tube 6,687 mm long with an outer diameter of 

139.7 mm and a wall thickness of 15.9 mm. The steel tube was covered with a white HDPE tube 

6,198 mm long with an inner diameter of 141 mm and a mean outer diameter of 161.7 mm. 

Two hatches were cut in the steel pipe and HDPE tube to allow for the installation of the surface 

pressure taps, pneumatic tubing, and electronic pressure transducers.

8
The main characteristics of the model were as follows:

• Mean diameter: 161.7 mm.

• Length-to-diameter ratio: 38.5.

• Surface roughness: Sanded HDPE surface with repaired scratches and roughness depthto-diameter ratio of ≈ 6.5×10-6

.

Visual inspection of the model revealed that the outside geometry of the HDPE tube was not 

perfectly round. To characterize its relative eccentricity, the outside diameter of the model was 

measured at every 10 degrees of azimuth at four span-wise locations, which correspond to the 

location of the four rings of surface pressure taps. The results are presented in figure 4. The 

largest observed deviation was equivalent to 1 percent of the mean diameter with four distinct 

regions alternating from peak to valley. Flamand and Boujard have reported a similar profile for 

a HDPE tube and suggest that the method of production of the tube using extrusion results in a 

shape that differs systematically from a circle.(8)

Figure 4. Graph. Variations of the cable model diameter with azimuth at four span-wise 

locations.

A helical fillet with a rectangular cross section 2.3 mm high and 2.4 mm wide was fixed in a 

right-handed direction to the surface of the model with double-sided tape that was 0.1 mm thick. 

The geometry was selected to represent as close as possible what is used in practice as presented 

in table 1. A double parallel helix with a pitch of 520 mm was used with a helix angle of 

44.5 degrees (See figure 5 and figure 6). The method of installation of the helical fillet was 

selected so that it could be removed without marking the external surface of the HDPE tube.

9
Figure 5. Photo. Close-up view of double helical right-handed fillet.

Figure 6. Photo. Overview of double helical right-handed fillet.

SUSPENSION SYSTEM

The sectional model rig used for the two previous experiments with an inclined cable in the same 

test facility was also used for the present study.(7) The only modification that was made to the rig 

was to allow rotation of the cable model on its axis without a rotation of the spring plane. In the 

previous experiments, it was possible to rotate the cable on its axis by rotating the spring plane, 

therefore changing two parameters at the same time. In light of the variations of diameter shown 

in figure 4, it was considered important to keep the rotation of the model on its axis as an 

independent parameter.

10
The suspension system was composed of eight springs and one axial suspension cable. The rig 

allowed for motion of the cable in two orthogonal planes, with four springs per plane, which is 

described as sway for a nominally across-wind motion and heave for a nominally along-wind 

motion. The springs were set on two large drums and tensioning frames, one for each extremity 

of the model, known as the lower and upper rigs (see figure 7 and figure 8). The stiffness of each 

spring could be adjusted by changing the number of active coils. The tension in each spring 

could also be adjusted using a threaded rod pulling system. The orientation of the spring planes 

with the flow could be changed by rotating the large drums of the lower and upper rig on their 

axes. Finally, by changing the position of the upper rig in relation to the lower rig, the inclination 

of the model could be changed.

Figure 7. Photo. Lower rig with spring rotation at 0 degrees.

Figure 8. Photo. Upper rig with spring rotation at 45 degrees.

The axial suspension cable linked the top end of the model to a cross beam at the ceiling of the 

wind tunnel building. Its role was to take a large part of the weight of the model, preventing it 

from sliding downwards. The length and the angle of the axial cable in relation to the model 

11
were fully adjustable. Figure 9 and figure 10 show overall views of the experimental setup.

In figure 9, the red arrow above the wind tunnel roof points to the axial cable supporting 

the model.

Figure 9. Photo. Cable model at an inclination of 60 degrees from outside the test section of 

the 3-by-6-m Propulsion and Icing Wind Tunnel. 

12
Figure 10. Photo. Cable model at an inclination of 60 degrees from inside the test section of 

the 3-by-6-m Propulsion and Icing Wind Tunnel.

To allow for rotation of the model on its axis, two small turntables were added to the flanges that 

link the extremities of the model to the springs (see figure 11). The model was set free to rotate 

on its axis by simply loosening two set screws at its extremities. Any rotation was possible.

Figure 11. Photo. Turntable that allowed rotation of the cable model on its axis.

Because all springs were identical, it was possible to adjust their axial stiffness by carefully

controlling the number of active coils. For each spring, a steel perch could be threaded in and out 

13
of the springs, therefore freeing or locking out a set number of coils. From the 2001 inclined 

cable study, it was established that 28 active coils corresponded to an axial stiffness of 

4.78 kN/m.(4,5) From the 2008 study, it was observed that the axial cable contributed to a nonnegligible part of the stiffness of the upper rig.

(6,7) At an inclination angle of 60 degrees, the 

tension in the axial cable contributed to a stiffness of approximately 1.0 kN/m.

To maintain the previous oscillation frequencies (≈ 1.41Hz) and frequency ratio (≈ 1.02 sway-toheave) as well as the upper and lower rig stiffness, the springs were adjusted to the number of 

active coils as shown in table 2.

Table 2. Number of active coils per spring.

Springs

Sway

(Two Springs)

Heave

(Two Springs)

Upper rig 28.00 26.75

Lower rig 24.38 25.38

Each spring was pre-tensioned independently to ensure a linear motion for the entire range of 

vibrations expected during the tests. The level of tension in the springs in one plane affected the 

frequencies of oscillations in the other plane, so care was taken to adjust the tension through a 

control of the spring extension when the model was at rest.

Taking into account the masses of the steel core of the model, the HDPE tube, the 

instrumentation, the links between the model and the springs, and one-third of the mass of 

the active part of the springs, the suspended mass was established at 407 kg for this study in 

accordance with the 2001 and 2008 mass estimates. (See references 4–7.) The distance between 

the two spring planes was fixed at 6,858 mm. As stated earlier, the length of the steel core of the 

model was 6,687 mm. However, the length of the model exposed to the flow was slightly shorter

at 6,100 mm for the 60-degree inclination case. The mass per unit exposed length of the cable 

model was therefore equivalent to 66.7 kg/m. Table 3 summarizes the dimensions of the cable 

related to its length or to the distance between lasers used at both extremities of the cable.

Table 3. Cable length or distance for instrumentation at both extremities of the cable.

Measurement Length (mm)

Cable length (polyethylene part) 6,198

Cable length (steel part) 6,687

Distance between spring planes 6,858

Distance between displacement transducers for sway 7,116

Distance between displacement transducers for heave 7,285

Representative exposed cable length at 60-degree inclination 6,100

Representative exposed cable length at 45-degree inclination 6,000

The upper end of the model pierced through the roof of the wind tunnel. The lower end of the 

model and the lower rig were fully immersed in the flow. For the majority of the tests, the 

circular hole at the interface between the roof and the model was kept open and allowed model 

displacement of approximately 120 mm. For one case, the hole was sealed to identify the 

influence of the end conditions on the mean aerodynamic characteristics of the cable model. 

Figure 12 and figure 13 show the top end of the model.

14
Figure 12. Photo. Top of the open interface between the cable model and the roof of the 

wind tunnel.

Figure 13. Photo. Underside of the sealed interface between the cable model and the roof of 

the wind tunnel.

FLOW CONDITIONS

Smooth Flow

All tests were carried out in the NRC-IAR 3-by-6-m Propulsion and Icing Wind Tunnel in 

Ottawa, Canada. This test facility is an open circuit wind tunnel of the blowing type. A 7.9-mdiameter 16-blade fan draws outdoor air and pushes it through a large settling chamber followed 

by a 6:1 ratio contraction before entering the 12.2-m-long test section. The fan is fitted with a set 

of anti-swirl stators, and the settling chamber has a set of fine mesh screens to keep flow 

turbulence to a minimum. The test section is followed by a diffuser with a 90-degree bend and 

exhausts directly outdoors. The test section is 3.05 m wide and 6.1 m high. It is equipped with 

removable fillets reducing in size in the direction of the flow to mitigate stream-wise pressure 

gradients associated with growth of the wall boundary layers. The entire floor of the test section 

is mounted on jacks and can be raised by 2 m.

The fan is powered by a 750-kW direct current motor, providing a maximum wind speed of 

39 m/s for the empty test section. The wind speed is controlled by increasing the fan revolutions 

per minute, which can be done in small increments, allowing a fine adjustment of the mean wind 

15
speed when outdoor conditions are calm. In gusty conditions, the wind speed inside the test 

section can experience low frequency modulation for wind speed below about 14 m/s.

For the present study, only the fillets of the test section roof where installed. Prior to the 

installation of the cable model, a calibration of the test section dynamic pressure in relation to the 

pressure difference between the settling chamber and the test section inlet was carried out. The 

latter was measured during the entire investigation to provide the test section dynamic pressure 

and wind speed. Figure 14 shows a downstream view of the configuration of the test section 

during calibration.

Figure 14. Photo. Downstream view of the test section during dynamic pressure calibration 

prior to the installation of the cable model.

The turbulence intensity of the flow was measured throughout the tests at the entrance of the test 

section, 4 m above the floor, using a Turbulent Flow Instrumentation (TFI) Cobra Probe, which

provides, with a high sampling frequency, the three unsteady components of the wind speed and 

the turbulence characteristics of the wind. For mean wind speeds above 14 m/s, the turbulence 

intensity varied between 0.35 and 0.5 percent. For lower wind speeds (8 to 12 m/s) in calm days 

outdoors, similar turbulence levels were observed. On windy days, the turbulence level below 

14 m/s generally increased and was typically in the 0.7 to 1.2 percent range. Figure 15 compares 

the variations of longitudinal turbulence intensity (Iu) with wind speed for the smooth flow case 

on a calm day versus a windy day.

16
Figure 15. Graph. Variations of Iu with wind speed measured at the entrance of the test 

section for different external conditions for the smooth flow case.

Turbulent Flow

The test program included experiments in turbulent flow for the cable model with a 60-degree

inclination. The objective was to study the aerodynamics of the cable with and without the 

helical fillet in a uniform flow field with turbulence characteristics representative of conditions 

found in the field.

The following characteristics were deemed important to consider in the definition of the 

turbulence field to use:

1. Turbulence level between 3 and 6 percent.

2. Turbulence integral scales larger than the expected boundary layer thickness at the surface of 

the model and larger than the thickness of the helical fillet.

3. Relatively uniform turbulence along the length of the model.

4. Turbulence spectrum with a representative level of energy at high frequency (i.e., with a 

representative energy level for the small scale turbulence).

Given the limited length of the test section in relation to the length of the model, it was not 

possible to use large vortex generators such as large bar lattice structures, spires, or panels far 

ahead of the model and let this turbulence stretch in the test section before reaching the model. It 

was also not possible to use a rope net or mesh with a small bar size and mesh size to fulfill 

characteristics 2 and 4.

17
To obtain a uniform turbulence level, a grid had to be used. However, since the turbulence level 

decayed rapidly as the vortices traveled downstream, the grid could not be installed vertically at 

the entrance of the test section like it is commonly done. The turbulence level at the top of the 

model (closer to the grid) would have been larger than the turbulence level at the bottom of 

the model, which was approximately 3 m downstream of the top of the model. To fulfill 

characteristic 3, the grid had to be installed parallel to the cable (i.e., inclined at 60 degrees from 

the floor). The bar size of the grid had to be large enough to produce eddies bigger than the 

helical fillet cross section, and the mesh size had to be small enough to promote flow mixing 

downstream. The logistics of installing a turbulence grid inclined at 60 degrees and with enough 

strength to sustain 39 m/s winds for a long period suggested the use of a light metallic structure.

Five aluminum ladders 6.4 m long were fastened together and lifted in place in parallel to the 

model. The ladders spanned the entire height of the test section and 80 percent of the width. 

They formed a quasi-uniform grid with a bar size of 35 mm and mesh size of 305 mm. Two 

positions upstream of the model were investigated. The first position was 3.3 m upstream and

had a turbulence level above the limit defined in characteristic 1. The second position was 5.1 m 

upstream of the model and had a mean turbulence level of 3.5 to 4.5 percent and was retained as 

the solution for the tests. Figure 16 and figure 17 show downstream views of the ladder grid for 

the two investigated positions.

Figure 16. Photo. Grid of ladders used to generate the turbulent flow field for position 1.

18
Figure 17. Photo. Grid of ladders used to generate the turbulent flow field for position 2. 

A TFI Cobra Probe was used to document the turbulent flow field behind the ladder grid. The 

cable model was used to support the probe at several heights above the floor (see figure 18). The 

probe was mounted 430 mm in front of the model.

Figure 18. Photo. TFI Cobra Probe attached to the cable model to measure the turbulence 

level behind the grid of ladders.

Figure 19 and figure 20 present the results of the measurements of the oncoming turbulent flow 

field for the turbulent flow test cases. The integral scales of the turbulence, calculated using the 

autocorrelation function approach, were as follows: longitudinal, x

Lu = 90 mm, lateral, xLv = 

47 mm, and vertical, xLw = 46 mm. The turbulence length scales were 40 times larger than the 

19
size of the helical fillet for the longitudinal components of the flow and 20 times for the 

other directions.

Iu = Longitudinal turbulence intensity.

Iv = Lateral turbulence intensity.

Iw = Vertical turbulence intensity.

Figure 19. Graph. Variations of the normalized spectral densities of the wind velocity 

fluctuations with frequencies for the smooth and turbulent flow cases.

Figure 20. Graph. Vertical and lateral profiles of the intensity of turbulence for the three 

wind components for the turbulent flow for position 2.

The left graph in figure 20 presents the variations of the turbulence intensity with height at the 

model location. The turbulence intensity was uniform along the length of the model with the 

exception of a slight increase at the wind tunnel mid-height corresponding to a region where the 

grid of ladders had a higher density. The ladders forming the upper part of the grid overlapped 

with the ladders forming the lower part of the grid over a 1.5-m section at the center of the wind 

20
tunnel. The lateral uniformity of the turbulence (right graph of figure 20) was also acceptable

with the exception of an increase in turbulence level near the starboard wall. Within a region 

of ±4 cable diameters from the model centerline, the flow turbulence can be considered 

uniform laterally.

21

CHAPTER 3: EXPERIMENTAL PROCEDURES AND ANALYSIS

TEST PROGRAM

The experiments were carried out in two distinct phases. The focus of the first phase was to 

identify any potential divergent vibrations for the cable model with a helical fillet at an 

inclination of 60 degrees for various rotations of the model on its longitudinal axis and spring 

rotations. In the event that vibrations would be identified in the first phase, the focus of the 

second phase would be to define the level of structural damping necessary to mitigate the 

vibrations and to define the effect of adding turbulence to the oncoming flow on the vibrations. 

In addition, tests in the second phase were to be carried out to look for other divergent vibrations 

at other inclination angles and spring rotations with the helical fillet in place.

The exploratory nature of the experiments resulted in the original test program evolving over 

time. The findings of the day were used to define the tests for the next day as well as for the 

entire duration of the investigation. The original main objective, which was to define the 

aerodynamics of the cable model fitted with a helical fillet as a function of wind speed and 

model attitude to the flow, was reached. Tests were added to link the present study with the 

two previous studies at NRC-IAR on a smooth cable in 2001 and 2008. (See references 4–7.) For 

this, the helical fillet was removed for the last 4 days of the investigation, and tests on the smooth 

model in smooth and turbulent flow at 60 degrees were carried out.

Two inclination angles were investigated, 60 and 45 degrees. The former was selected as the 

prime inclination to study since it was identified in previous experiments as having aerodynamic 

characteristics in the critical Reynolds number range most likely to lead to instability for a 

smooth stay cable. The latter was selected since the flow on one side of the model is fully 

perpendicular to the helical fillet. A large asymmetry in the pressure field was thus anticipated, 

resulting in a steady across-wind force that could possibly vary within the critical regime.

The test program is outlined in table 4, and a detailed run log is presented in appendix A.

23
Table 4. Summary of test program for phases I and II.

Day Run

Inclination

(degree)

Spring 

Rotation 

(degree)

Cable 

Rotation 

(degree) Case Comments

Phase I

1 27, 28 60 0 0 Dynamic Increasing and 

decreasing wind speed

2 32, 35, 37 60 0 0, 0, 27.7 Static Increasing and 

decreasing wind speed

3 39, 41 60 0 -13.8, 13.8 Static

44, 46 60 0 -13.8 Dynamic 46 is a repeat of 44

4 49, 52 60 0 -30, -40 Dynamic

56, 60 60 0 -50, -60 Dynamic

5

63, 66, 67 60 0 -75, -90, -90 Dynamic 67 has decreasing wind 

speed

69, 71 60 0 5, 65 Dynamic

6 73, 75 60 0 50, -90 Dynamic 75 is a repeat of 66

81, 85 60 0 -90, -86 Static

7 88, 90 60 0 -88, -92 Static

92, 94 60 0 -94, -90 Static 94 is a repeat of 81

8

108 60 0 -90 Dynamic Medium damping

118, 122, 123 60 0 -90 Dynamic High and low damping

123 60 0 -90 Dynamic Decreasing wind speed

Phase II

10 125, 131 60 0, -54.7 -88, -90 Dynamic

12 136 60 0 -90 Dynamic

13 137, 140 45 0 0, 90 Dynamic

142, 144 45 0 27, -25 Dynamic

15 149, 152 45 -54.7 -25, 0 Dynamic

155 45 -45 -25 Dynamic

16 159 45 -12.5 -25 Dynamic

18 163 60 -12.5 -90 Dynamic Windy

22 167 60 -12.5 -90 Dynamic 167 is repeat of 163

23 176, 178 60 0 -92, -90 Dynamic

27 197, 199 60 0 -90, -92 Dynamic Turbulent flow

28 203, 205, 208 60 0 -88, 0, 50 Dynamic Turbulent flow

30 211, 214 60 0 50, 0 Dynamic Turbulent, no helical 

fillet

31

216, 219, 222 60 0 -90, -88, -92 Dynamic Turbulent, no helical 

fillet

225, 226 60 0 -54.7 Dynamic Turbulent, no helical 

fillet

32 230, 233 60 0 -57.7, 0 Dynamic Smooth, no helical fillet

237, 239 60 0 -2, 2 Dynamic Smooth, no helical fillet

33 244 60 0 2 Dynamic Smooth, no helical fillet

24
248, 250 60 0 -93 Static Top gap open and 

sealed

253, 255 60 0 -93, -90 Dynamic Smooth, no helical fillet

257, 260 60 0 -88 Dynamic 10–90 s sampling

262, 263 60 0 -88 Dynamic 12-22 m/s, ramp up

The spring rotation angles were selected to represent common field conditions based on the 

relationships defined in 2001.(9) The model inclination ( ) and spring rotation ( ) relate to stay 

cable inclination ( ) and the flow yaw angle ( ) through the following equations:

Figure 21. Equation. Model inclination.

Figure 22. Equation. Spring rotation.

Using these relationships, a model inclination angle of 60 degree and a spring rotation of 

-54.7 degrees correspond to a stay cable inclination of 45 degrees and yaw angle of 45 degrees. 

Table 5 presents the relationships for the other cases where a rotation of the spring plane was 

carried out during the tests. A negative sign for the spring and cable rotation was related with a 

clockwise rotation when looking down along the cable axis.

Table 5. Relationship between model wind-angle planes and field conditions.

Run

Model Experiments Field Conditions

Inclination

(degree)

Spring Rotation

(degree)

Inclination

(degree)

Yaw

(degree)

131 60 -54.7 45 45

149, 152 45 -54.7 30 35

155 45 -45 35 30

159 45 -12.5 44 8

163, 167 60 -12.5 59 11

INSTRUMENTATION

All electronic equipment used for the tests was specifically calibrated for this project or verified 

by the expert technical staff in conformity with NRC-IAR’s quality assurance procedures which 

are compliant with ISO 9001-2008.

The dynamic pressure in the test section was obtained from two independent pressure 

measurements using two differential pressure transducers. Two parallel measurements were 

made for redundancy. The temperature of the flow in the settling chamber and the barometric 

pressure at the inlet of the test section were also recorded for each run. As described in the 

section on smooth flow in chapter 2, a test section calibration was carried out to relate the 

recorded flow characteristics to the wind speed at the model location in the center of the 

test section.

φ α

θ β

φ α θ β

25
The sway and heave motion at the extremities of the cable model were measured with laser 

displacement transducers. Four transducers were used, one pair per each end of the model. The 

laser sensing heads were placed approximately 250 mm away from the targets fastened to the 

spring restraining rods. The distance between the sway sensors was 7,116 mm, and the distance 

between the heave sensors was 7,285 mm. Four accelerometers were also used in parallel with 

the displacement transducers to provide a redundant monitoring of the motion. The heave and 

sway motion were calculated by directly averaging the two time histories of displacements per 

mode. The end-to-end motion in both directions was calculated by subtracting the time histories 

of the displacement signals at the extremity of the models.

All analogue outputs from the laser transducers and accelerometers were low-pass filtered prior 

to being sampled simultaneously at frequencies of 500 or 2,500 Hz with a National Instruments®

VXI 1629 data acquisition system and LabVIEW® custom-made software. The sampling time 

was typically 90 s and was increased to 300 s for the damping tests.

Two TFI Cobra Probes were used for the tests in smooth flow to monitor the flow fluctuations. 

A sampling frequency of 2,500 Hz was used when the signal from the TFI Cobra Probes were 

recorded and 500 Hz when the probes were not in use. Each probe monitored three components

of the flow fluctuations: longitudinal, lateral, and vertical. Both probes had sturdy probe holders 

cantilevered from the south wall of the test section. One probe was installed at the inlet plane of 

the test section to monitor the fluctuations of the oncoming flow. The second probe was installed 

behind the model at the center of the test section to monitor the flow fluctuations in the wake at 

the same height as the ring 3 pressure sensors. The tip of the probe in the model wake was 

located 403 mm behind the cable model and 5 mm inboard of the model edge on the port side. 

The probes had an acceptable frequency response in excess of 1,500 Hz and were capable of 

capturing low- and high-frequency fluctuations of the flow.

As was done for the 2008 experiments, the cable model was instrumented with 160 pressure taps. 

The pressure taps were arranged in 4 cross-sectional rings of 32 taps and 2 longitudinal lines of 

16 taps as shown in figure 23.

(6,7) Four electronic pressure scanners (Scanivalve Inc.® ZOC 33 

and ZOC 23b) were embedded directly in the model to keep the length of the pneumatic tubing 

to a minimum. Lengths of tubing of 1.2 m were used systematically for all taps. The frequency 

response of each pressure tap and tubing system was measured prior to the 2008 experiments and 

was reused for this study to correct for the distortion of the pressure signals due to the tubing. A 

detailed description of the pressure measurements of the 2008 experiments is given in Andersen 

et al., Andersen, Nikitas et al., and Jakobsen et al. (See references 6, 7, 10, and 11.)

26
d = Nominal cable diameter of 160 mm.

U = Flow direction.

L = Lift direction.

D = Drag direction.

Figure 23. Illustration. Sketch of the pressure tap arrangement. 

The pressure signals from the scanners were monitored using a Scanivalve Inc.® RAD system 

and a dedicated data acquisition system independent of the National Instruments® VXI 1629 

system described previously. The pressure signals were sampled at a rate of 312.5 Hz for 90 s. 

The analog signals from the laser displacement transducers and the accelerometers were also 

monitored by the surface pressure data acquisition system to provide synchronous recordings of 

pressure field fluctuations and corresponding motion of the cable model. In addition, a square 

wave analog signal was monitored by both the National Instruments® VXI 1629 and the surface 

pressure data acquisition system to allow a precise synchronization of both systems. This way, 

the fluctuations of the flow in the wake of the model captured with the TFI Cobra Probe could be 

associated with the pressure fluctuations at the surface of the cable model.

TEST PROCEDURES

Two types of experiments were carried out during this study: dynamic and static tests. Prior to 

any testing, a thorough inspection of the cable model was carried out to ensure that dirt, small 

bugs, or small leaves had not been left on the model from the previous test series. If any were 

found, the model was systematically cleaned. Inspection of the helical fillet was also carried out 

to ensure that it remained affixed to the model surface during the experiments. The fillet had a

tendency to lift from the surface during cold weather conditions. Figure 24 shows a typical 

model inspection.

27
Figure 24. Photo. Model inspection in the test section.

For the dynamic tests, a wind-off value of all transducer signals was first recorded with the doors 

of the wind tunnel test section closed. With the doors open, flow is generally present in the test 

section given the open circuit of the wind tunnel. Subsequently, the wind speed was increased 

to a desired value displayed continuously from the data acquisition system, and the model 

displacements and acceleration were graphically displayed on a screen in the control room. 

Once a steady state wind speed and model response were reached, the operator started the data 

acquisition process. Once the 90-s data acquisition was completed, the wind tunnel operator 

increased the wind speed to the next set point. Small increments of wind speed were used, 

generally 1 or 2 m/s depending on the observed behavior of the cable model. The wind speed 

sweeps generally covered the entire range of wind speed possible in the facility, from 4 to 36 m/s 

in 16 to 18 points. Unless otherwise specified, the wind speed sweeps were carried out with 

positive increments of wind velocity.

In the event that the wind tunnel operator observed a growth of the vibration after 90 s of data 

acquisition, a second recording was initiated at the same wind speed. For selected cases at high 

wind speeds, the motion of the model was manually stopped and released to identify the rate of 

growth of the oscillations. For some of the same cases, the model was excited manually to a high 

amplitude, and the decay or growth of the vibrations was monitored for 90 s.

The growth of the motion was first captured by manually preventing the cable model to move, 

starting the acquisition of the data, and finally letting the model move freely. The decay traces 

were captured by first manually imposing cable motion with large amplitude in the first sway 

mode, starting the data acquisition, and finally letting the model move freely. In both cases, 

28
traces of the displacement of the cable with time could be analyzed, and aerodynamic damping 

characteristics could be extracted.

An example of a trace measured for the sway mode for the cable with the helical fillet inclined at 

60 degrees and rotated at -88 degrees is presented in figure 25. It only took a few seconds for the 

cable to start building energy and to vibrate with high amplitude even if the effective sprung 

mass was as high as 407 kg, and the oscillation frequency was 1.4 Hz. It has been reported that 

for previous tests done with the same cable model in 2001 and 2008, the aerodynamic response 

of the cable took much longer to build up. (See references 4–7.) In this present case, the cable 

was prompt to respond, inferring strong negative aerodynamic damping. The presence of the 

helical fillet, the wind speed at which the motion took place and the frequency ratio of 1.0 

between the sway and heave modes could have had a role to play with this observation.

Figure 25. Graph. Growth of the cable model vibration as a function of time inclined at 

60 degrees and rotated at -88 degrees.

Another example of an increase of vibrations is shown in figure 26. It corresponds to vibrations 

in the sway mode for the cable with helical fillet inclined at 60 degrees and rotated at -90 degrees 

with no spring plane rotation. In this case, the growth of the vibration in the sway end-to-end 

mode was rapid and appeared to dominate the motion.

29
Figure 26. Graph. Growth of the cable model vibration as a function of time inclined at

60 degrees and rotated at -90 degrees.

Each dynamic test took between 1.5 and 2 h. Prior of the dynamic tests, the structural damping of 

the suspension rig was established through 300-s decay tests in still air. The structural damping 

of the cable model and suspension system was evaluated in situ by analysis of decay traces. The 

model was manually excited at its natural frequency in each mode. When the desired amplitude 

was reached, the model was released to obtain a smooth decay trace using optical displacement 

transducers at the model extremities. Piece-wise linear fit of the Hilbert transform of the decay 

signal in blocks of 10 s produced the amplitude of vibration versus damping curve as presented

in figure 27.

Figure 27. Graph. Example of decay trace for the sway mode of vibration and 

corresponding variation of damping with amplitude of vibrations.

30
For the static tests, steel locking pins were inserted at the extremities of the cable model to 

restrain oscillations. A tare of the surface pressure transducers was carried out with the doors of 

the test section closed. The wind speed was then increased to a desired value. Once a steady state 

wind speed was reached, the operator started the data acquisition process. The tests were 

repeated for 13 to 15 mean wind speeds.

The test program included several rotations of the cable model on its longitudinal axis 

(see table 4). The following procedures were used to adjust the angle to a prescribed value 

as illustrated by figure 28:

1. The prescribed angle was marked on the cable model.

2. The locking pins were inserted at the bottom end of the model to prevent sway or 

heave motion.

3. A self-leveling laser beam was projected along the length of the model to mark its center.

4. The turn-table at each end of the model was unlocked.

5. The model was manually rotated until the mark of the prescribed angle intersected with the 

laser beam.

6. The turn-table at each end of the model was locked, and the locking pins were released.

Figure 28. Photo. Procedures followed to set the azimuth angle of the cable model.

31
DATA ANALYSIS AND REPORTING

Preliminary data reduction was performed at the end of each run using a dedicated MATLAB®

program as follows:

• The tare values were subtracted from the wind-on data.

• The signal was converted to engineering units.

• Wind speed was calculated based on the measured dynamic pressure including 

corrections for temperature and atmospheric pressure.

• Combination of channels were made (addition or subtraction) to provide sway and heave 

responses from the displacement and acceleration measurements.

• Statistics (mean, root mean square, maximum, and minimum) were calculated.

• The surface pressure signals were corrected for the distortion caused by the pneumatic 

tubing, and pressure coefficients were calculated.

• The surface pressure distributions were integrated to calculate mean and fluctuation force 

coefficients.

• Graphs of response and load coefficients were produced to allow a fine diagnostic of the 

acquired data as the tests proceeded.

• All time histories were stored in a binary file in MATLAB® format for each point.

• Natural frequencies and structural damping were extracted from the decay traces.

Post processing of the data using MATLAB® was carried out. The following additional data 

reduction was carried out:

• Spectral analysis of all time histories was carried out.

• The modal frequency and structural damping were extracted from each decay test.

• The stiffness of the suspension rig was calculated for each mode, and the cross sectional 

static mean load coefficients as a function of wind speed were calculated based on the 

mean displacements of the entire model.

• All processed data were added to the output binary files for further analysis.

• A detailed run summary including frequency and damping estimates was made 

(presented in appendix A).

32
CHAPTER 4: RESULTS AND DISCUSSION OF EXPERIMENTS

GENERAL

A two-page graphical summary of the results collected is presented in appendix B for each test 

run defined in table 4 (see figure 59 through figure 183). For the dynamic tests, the graphs 

present the variation of the response of the model for four modes of oscillations as a function of 

wind speed and Reynolds number. The four modes of oscillations are: (1) the sway (acrosswind), (2) heave (along-wind), (3) first modes where both ends of the cable model moved in a 

synchronous manner, and (4) end-to-end modes (sway and heave) where the model extremities 

were out of phase with each other. The Reynolds number in the graphs is based on the mean 

wind speed as measured in the frame of reference of the wind tunnel and the cable model mean 

diameter, D = 161.7 mm.

The response given in the graphs corresponds to the maximum amplitude of motion of the cable 

model both from the displacement transducers and from the accelerometers during a 90-s period 

at the mean wind speeds indicated in the graphs. For the same period of time and experimental 

conditions, the graphs in appendix B show the following parameters as a function of Reynolds 

number as follows:

• The variations of the mean force coefficients, along-wind (Cx) and across-wind (Cy),

calculated from integration of the surface pressure for each of the four cross-sectional 

rings of taps.

• The average of the four sets of mean force coefficients for both directions.

• The static force coefficients calculated from a conversion of the mean cable displacement 

during a run for each direction to an equivalent mean force based on the dynamic 

stiffness of the suspension system and normalized by the dynamic pressure and the 

frontal area of the entire cable model.

• The variations of the mean displacements of the cable model with wind speed.

• The peak factor of the response defined as the maximum amplitude divided by the 

standard deviation (root-mean-square) of the measured signal.

• The along wind and across wind trajectories of the cable model at a strategically selected 

wind speed.

• The variations of the longitudinal turbulence level of the oncoming flow as measured at 

the inlet of the wind tunnel for each of the wind speeds in smooth flow.

When specific test conditions did not apply (e.g., when the cable model was locked for the static 

tests), the appropriate graphs were left blank.

The two main findings of the first phase of the investigation were: (1) a stay cable with a typical 

helical fillet and inclined at 60 degrees to the flow can sustain wind-induced vibrations in smooth 

33
flow, and (2) the amplitude of the cable vibrations observed were greatly influenced by the 

geometry of the HDPE tube, whereby a rotation of the cable model on its longitudinal axis could 

translate into vibrations with unacceptable amplitudes or vibrations with small amplitude.

The first finding is new (i.e., it has not been reported elsewhere). It was not expected since the 

general belief was that the helical fillet would reduce the sensitivity of the aerodynamics of the 

model to Reynolds number effects in the critical regime, which is believed to be a primary cause 

of inclined cable galloping. It might explain observations of stay cable vibrations of cables with 

a helical fillet in dry conditions as reported in field measurement campaigns. The oscillations 

were not caused by buffeting due to turbulence and were similar to high reduced velocity vortex 

shedding.

(4) The oscillations occurred in some cases at higher wind speeds than what were 

reported earlier for a smooth cable, in a Reynolds number range above what is generally 

considered the critical range for which the static coefficients do not vary significantly with 

wind speed.

The second finding is also unique and strongly affected the course of the tests. However, it was 

anticipated based on the observations reported by Flamand and Boujard who pointed out the 

systematic deviation of general HDPE tubes from a circular shape and its possible corresponding 

consequences on the mean aerodynamic force coefficients.

(8) The test cable cross sectional shape 

exhibited the same type of asymmetry as measured at four longitudinal positions (see figure 4). 

The measurements showed deviations of up to 1 percent of the mean cable diameter. The 

location of the deviations around the circumference appeared to be consistent along the length of 

the model, suggesting that they were formed during the extruding process of the HDPE tube or 

during its long-term storage. If an asymmetric pressure distribution can be observed on a smooth 

round model in the critical regime due to the formation of a small laminar separation bubble on 

one side of the model and not on the other, as reported in Larose et al., it is understandable that a 

mildly asymmetric cable shape will have complex aerodynamic properties in the same critical 

Reynolds number regime.(12)

Based on the second finding, it was concluded that each time the cable was rotated on its axis, a 

new shape was exposed to the flow, and a different behavior could be expected. This affected 

the test program greatly since originally it was planned to rotate the cable model on its axis at 

four azimuths, 0, 13.8, -13.8, and 27.7 degrees, to obtain a clear understanding of the mean force 

coefficients based on the integration of the surface pressures at four rings. These four azimuths 

were selected so that three of the four rings of pressure taps for each azimuth would be located at 

three different cross-sectional locations in relation to the helical fillet.

In four cable rotations, 12 different cross sections of the model with helical fillets would 

have been covered. Assuming that the model was symmetric, it was believed that a reliable 

representation of the quasi-steady aerodynamics of cable model would come from the 

average of cross-sectional coefficients of the four rings for four azimuths (i.e., the average of 

16 measurements). However, since the cable model was not symmetric, this averaging across the 

four azimuths was not sufficient to represent the aerodynamics of the entire model. Several of the 

static tests, designed to provide the quasi-steady aerodynamics of the cable model, were replaced 

by dynamic tests at various additional model rotations.

34
INFLUENCE OF THE ATTITUDE OF THE CABLE TO THE MAIN WIND FLOW

Influence of the Cable Rotation

As described in the “Suspension System” section in chapter 2, a new feature of the mechanical 

setup of the cable allowed for the rotation of the cable along its main axis without changing the 

spring plane angle, therefore not affecting the wind-angle plane and the main direction of motion 

of the cable. An evaluation of the response of the cable for different angles of rotation was 

carried out. While the original plan was to perform only a few angles to identify the azimuth 

for which the largest response of the cable was observed, the differences in the results led to a 

reconsideration of the number of azimuth angles to be selected for performing the measurements.

In fact, for the cable with the helical fillet and inclined at 60 degrees, in smooth flow 13 rotations 

of the cable were carried out from -92 to 65 degrees. Significant vibration of the model in the 

sway mode was observed for the cable rotated at angular positions of -92, -90, and -88 degrees. 

The angular position was defined as being 0 degrees when pressure tap 4 was the stagnation 

point, and a negative angle was associated with a clockwise rotation of the cable from a top view 

perspective. The 0-degree azimuth defined in this manner corresponded to the same 0 degrees of 

the 2001 and 2008 studies. (See references 4–7.) Large amplitude displacements in the first sway 

mode (across-wind) on the order of 30 to 75 mm were observed in the vicinity of -90 degrees but 

did not occur for the other rotations examined. Figure 29 shows the amplitude of motion in sway 

obtained for four different angles of rotation of the cable.

Figure 29. Graph. Amplitude of motion in sway for four different rotations of the cable 

along its main axis for the cable inclined at 60 degrees with helical fillet and in smooth flow.

The azimuth angles were picked through inspection of the cross-sectional profiles of the cable 

model shown in figure 4. It was theorized that a point of inflection in the cross-sectional profile 

that would be located in the vicinity of the point of separation of the boundary layer at the 

surface of the model could have an influence on the response, especially if this point of inflection 

was not symmetric between the two sides of the model. With figure 4 as a reference, when the 

35
azimuth of the model was set at -90 degrees, the point of inflection in the profiles centered at 

azimuth 4 degrees was at 94 degrees from the stagnation point and therefore likely near the area 

on the cable model where separation of the boundary layer could be expected. This surface 

deformation could have caused the boundary layer to separate earlier or later on one side of the 

cable or the other, creating fluctuating across-wind forces due to the motion of the model and 

undefined possible instabilities.

It is difficult to attribute the variation in the response of the cable model solely on its orientation 

or attitude to the flow as other factors might have contributed to affect the response. However, 

there is evidence that around a certain range of cable rotations, the model appeared to be more 

lively, inferring stronger wind excitation, stronger buildup of energy, and larger vibrations.

A similar verification of the influence of the model orientation on the wind induced response 

was carried out for the other configurations of the cable (i.e., in turbulent flow or for the cable 

without the helical fillet). Fewer angles of rotation were tested to evaluate the response of the 

cable under these other conditions and surprisingly, it was not only around -90 degrees that the 

cable moved considerably but also around 0, 50, and -54.7 degrees. Under the circumstances of 

this study, it is therefore difficult to predict the worst response of a stay cable without performing 

systematic measurements at multiple azimuth angles (over the 360-degree range) as the cable 

and its HDPE tube are not perfectly round and its behavior appeared to be strongly dependent on 

its attitude to the main direction of the wind. This conclusion also applies to a stay cable in 

turbulent flow or without a helical fillet since all those configurations have shown that the cable 

can give a different response depending on its angle of rotation. It is possible that larger sway 

vibrations could have occurred for the cable model of this study with rotation beyond the -94 to 

+65 degrees that was covered. It was out of the scope of work to look for the extreme response in 

relation to this parameter.

Influence of Cable-Wind Angle Plane

The baseline position of the upper and lower four-spring planes was 0 degrees, with four springs 

allowing mostly across-wind motion and four springs allowing mostly along-wind motion. The 

system of spring-planes could be rotated equally at the top and bottom of the cable model to 

modify the trajectory that the model would take in relation to the main flow direction, referred to 

here as the “cable-wind plane.” As for the 2001 and 2008 studies, it was possible to adjust the 

cable-wind plane to any desired values. (See references 4–7.) However, thanks to the new cable 

model turntables, it was possible to modify the cable-wind plane without affecting the attitude of 

the cable model to the flow. Both parameters (cable-wind plane and rotation of cable on its axis) 

could be changed independently, allowing the evaluation the effect of the cable-wind plane only 

on the response of the cable.

Tests were performed with the cable inclined at 60 degrees in smooth flow with the cable rotated 

at -90 degrees where strong vibrations were observed for a cable-wind plane of 0 degrees. The 

cable-wind angle plane was changed to -54.7 and -12.5 degrees. The angle of rotation of the 

spring plane was negative for a clockwise rotation of the system from a top-down point of view. 

The first angle of the spring plane of -54.7 degrees was chosen because it represents, in 

combination with a 60-degree inclination of the cable, a configuration identical to a 45-degree

inclination and 45-degree yaw of the cable, which is of interest for cable stay bridges as defined 

36
in table 5. This cable-wind plane was also studied in 2001 and 2008. (See references 4–7.)

The second spring angle of -12.5 degrees was selected based on the motion path of the cable 

observed when the spring angle was at 0 degrees; the cable was not moving perfectly in the 

across-wind direction but rather at -12.5 degrees from the across-wind axis (see figure 107 in 

appendix B).

Tests were performed for both additional cable-wind planes, keeping the angle of rotation of the 

model on its axis at -90 degrees. The tests indicated that the response of the cable was different 

depending on the spring plane angle. At 0 degrees, the cable was moving strongly with 

displacement around 75 mm at 36 m/s, while for the spring angle of -54.7 degrees (run 131), the 

cable was not oscillating significantly. This clearly demonstrated the importance of the relative 

angle between the motion of the cable and the wind, as anticipated by Macdonald and Larose.

(13)

For a spring angle of -12.5 degrees, two runs were performed. The first one (run 163) did not 

result in significant vibration of the cable, while the second run (run 167) had large amplitude 

displacements of 50 mm in the sway mode for the wind speed range of 22 to 36 m/s (see 

figure 30). The difference between the responses of the cable for those two runs is believed to be 

associated with the flow disturbance coming from outside of the test section. The first run was 

carried out during a very windy day, which affected the turbulence intensity of the oncoming 

flow on the cable, especially for wind speeds lower than 20 m/s. The longitudinal turbulence 

intensity was above 1 percent for speeds below 20 m/s. The variations of the mean wind speed 

due to this turbulence can affect not only the response of the cable for the low mean wind speeds 

but also the susceptibility of the cable motion to build and to undergo larger vibration at higher 

wind speed. The second run (run 167) was performed during a relatively calm day, with a 

longitudinal turbulence intensity measured at the entrance of the test section lower than 1 percent

for wind speeds higher than 5 m/s. Large displacements were observed, but the amplitudes did 

not exceed the amplitudes observed for a cable-wind plane of 0 degrees.

Figure 30. Graph. Amplitude of motion in sway for three different spring plane rotations 

for the cable inclined at 60 degrees with helical fillet and in smooth flow.

37
Additional analysis of the turbulence characteristics and its potential influence on the cable 

vibrations, which is beyond the scope of the present study, is recommended for these cases.

Influence of Cable Inclination

As part of the second phase of the investigation, the inclination of the model was changed from 

60 to 45 degrees (see figure 31). Comparison of the results obtained for both cable inclinations 

with the same cable rotation (-90 and 0 degrees) and cable-wind plane (0 degrees) was 

performed. It can be observed in figure 59, figure 106, figure 114, and figure 116 in appendix B

that the inclination of the cable did affect the response of the cable for a rotated angle of 

-90 degrees. At a 45-degree inclination, the cable did not oscillate significantly as it did for the 

cable inclined at 60 degrees where 75 mm amplitude displacement were observed at 36 m/s. 

At a 0-degree rotation of the model, no significant vibrations were observed for both 

cable inclinations.

Figure 31. Photo. Cable model at 45-degree inclination and 0-degree spring rotation with

smooth flow.

The mean force coefficients calculated from each ring of surface pressures revealed that the 

cable inclined at 45 degrees showed much less variation of the mean Cy as a function of 

Reynolds number compared to the cable inclined at 60 degrees (see figure 32). This observation 

was consistent with the mean Cy, which presented large variations for wind speeds lower than 

19 m/s, showing negative and positive values for the case of the cable at 60 degrees inclination.

At 45 degrees, Cy was stable with a more-or-less constant value between 0.2 and 0.5.

38
Figure 32. Graph. Mean force coefficients calculated from the integration of surface 

pressure measurements for the cable inclined at 60 and 45 degrees and rotated at 

-90 degrees along its main axis in smooth flow and with a helical fillet.

Several other tests were carried out for a cable inclination of 45 degrees with the helical fillet 

in place to look for galloping or other wind-induced vibrations. The model was rotated on 

its axis (-90, 0, 23, and -25 degrees) and the spring plane was also rotated (-54.7, -45, and

-12.5 degrees). No significant wind-induced vibrations were observed for a wind speed range of 

4 to 36 m/s for these cases. Since the cable model experienced more variations of its crosssectional force coefficients and larger amplitude of motion at 60-degree inclination, the focus of 

the second phase of the study was defined to investigate the factors that affect the behavior of the 

cable only for a 60-degree inclination.

INFLUENCE OF STRUCTURAL DAMPING

As reported earlier, tests at an inclination of 60 degrees with the helical fillet in smooth flow 

revealed large oscillations of the cable model in the sway modes at several wind speeds. 

Experiments were subsequently carried out to define the level of damping necessary to mitigate 

the vibrations. As per the 2001 tests, the structural damping of the suspension system was first 

increased by wrapping viscoelastic material (rubber bands) around the active coils of the springs 

(see figure 33).(4,5) Several rubber bands had to be used to increase by 66 percent the damping 

level. To obtain a larger increase of the damping level, adding rubber bands was not sufficient to 

reach a damping level corresponding to a Scruton number (Sc) of 5.0 or more. Scruton number is 

defined in figure 34.

39
Figure 33. Photo. Elastic bands used to increase the structural damping of the suspension 

system.

Figure 34. Equation. Scruton number.

Where:

m = Mass per unit length of the model. ζ = Damping ratio (fraction of critical damping). ρ = Air density.

d = Mean diameter of the model.

A Scruton number of 5.0 is used as a reference value by the Post-Tensioning Institute guidelines 

as the mass damping parameter level necessary to mitigate rain/wind-induced vibrations of stay 

cables with a helical fillet.(1) To reach a Scruton number greater than 5.0, washers covered with a 

visco-elastic material were inserted between the suspension rig frame and the locking nuts of the 

threaded rods that were used to control the tension in the springs (see figure 35). It was observed 

that the damping level of the suspension system was sensitive to the level of contact between the 

locking nuts and the frame, with a larger contact lowering the damping. By reducing the contact 

pressure through the compression of a viscoelastic material, the level of damping was increased 

to the desired value in a repeatable way.

40
Figure 35. Photo. Viscoelastic washer used to increase the structural damping of the 

suspension system.

Figure 36 and figure 37 show the variations of structural damping with amplitude for the 

three levels of damping examined for both the sway and heave modes respectively. The damping 

level were referred as follows: 

• Low: 0.08 percent at an amplitude of 30 mm (Sc = 1.6).

• Medium: 0.15 percent at an amplitude of 30 mm (Sc = 3.0).

• High: 0.25 percent at an amplitude of 20 mm (Sc = 5.1) for the sway mode, and 0.10 and 

0.15 percent for the heave mode at amplitudes of 10 mm. 

The graphs showing the actual decay traces for each case are presented in appendix B 

(see figure 184 through figure 186).

Figure 36. Graph. Structural damping level as a function of amplitude of motion of the 

cable for the sway mode.

41
Figure 37. Graph. Structural damping level as a function of amplitude of motion of the 

cable for the heave mode.

Figure 38 shows the response of the cable for three different levels of damping. The cable was 

oriented at 60 degrees from the horizontal with a wind-angle plane of 0 degrees. The cable was

rotated along its main axis to -90 degrees with the helical fillet and in smooth flow.

The graphs on the left side of figure 38 indicate the amplitude of motion as detected by the 

laser displacement and by the accelerometers. The amplitudes were obtained by averaging the 

maximum and minimum displacement or acceleration. Results indicate that a structural damping 

level of 0.25 percent (Sc = 5.1) in sway allowed a reduction the amplitude of displacement from 

75 to 25 mm or from 7 to 2 m/s2 at the maximum wind speed of 36 m/s. The graphs on the right 

side of figure 38 show that the mean forces acting on the cable (drag and lift force in the cable 

axis reference) were not significantly affected by the variation of damping level.

Figure 38 also presents results associated with a repetition of the same configuration at the low 

damping level case. It can be observed that the maximum amplitude of displacement was not 

repeated for both low damping level cases. One of the reasons could be linked with the variation 

of the turbulence intensity of the oncoming flow due to the wind conditions outdoors. The first

test where large amplitude was observed was done on a calm day (run 122) with longitudinal 

turbulence intensity generally low (0.5 percent from 19 to 36 m/s), while the repeat test where 

low amplitude was observed (run 178) was done on a windy day with more variation of the 

turbulence intensity as measured at the entrance of the test section and presented in figure 107

for run 122 and in figure 139 for run 178 (see appendix B).

42
Figure 38. Graph. Response of the cable model as a function of wind speed or Reynolds 

number for three damping levels as measured by lasers, accelerometers, and surface 

pressures for different levels of damping.

No other tests were carried out during the present investigation to evaluate the level of damping 

needed to mitigate the observed vibrations.

INFLUENCE OF TURBULENCE

Several tests were conducted in turbulent flow for the test section configuration described in the 

“Turbulent Flow” section in chapter 2 and shown in figure 39. The effect of wind turbulence on 

the response of the cable rotated at -90 degrees is presented in figure 40 through figure 43 for the 

cable with and without the helical fillet, respectively. The results indicate that a 4 to 5 percent

intensity of turbulence was not sufficient to mitigate the large vibration of the cable in the sway 

mode that was observed in smooth flow condition for a cable rotation on its axis between -88 and 

-92 degrees for the cable with or without a helical fillet. The turbulence seemed to reduce the 

amplitude of motion, and the vibrations took place at a lower wind speed compared to the 

smooth flow condition when the helical fillet was present.

However, large vibrations were observed in turbulent flow at higher wind speeds in the end-toend sway mode that were not present in smooth flow. The same observations were made for the 

cable without the helical fillet; end-to-end sway motion was strong and present for many of the 

configurations investigated in turbulent flow. It was accompanied by oscillations in the first sway 

mode, which were strong not only for cable rotations of -90 and -88 degrees but also at -54.7, 0, 

-2, and 2 degrees for the cable model without the helical fillet and at an inclination of 60 degrees.

43
The turbulence had a pronounced effect on the cross-sectional force coefficients, both for the 

cable model with the helical fillet and for the smooth cable. The effect was similar for the 

two cases, as illustrated in figure 41 and figure 43, for a cable inclination of 60 degrees and 

model rotation of -90 degrees.

For the case with the helical fillet, the turbulence reduced the velocity at which Cx reached its 

minimum by approximately 10 m/s. The rate of change of Cx with Reynolds number appeared to 

be slightly larger in turbulent flow than in smooth flow for parts of the drag crisis. Note that the 

larger the rate of change of the coefficients with Reynolds number, the higher the possibility of 

wind excitation from a quasi-steady aerodynamics point of view.

The turbulence appeared to have eliminated or at least greatly reduced the strong asymmetric 

pressure distributions in the wind speed range from 5 to 15 m/s that were causing the mean Cy to 

reach values around -0.45 in smooth flow. This can be considered as a stabilizing influence.

For the case of the smooth cable, the turbulence reduced (with even a larger margin) the velocity 

at which Cx reached its minimum. The lowest Cx was reached at a velocity 16 m/s lower in 

turbulent flow than in smooth flow. As for the case with the helical fillet, the rate of change of 

Cx with Reynolds number appeared to be slightly larger in turbulent flow than in smooth flow. 

For Cy, the smooth cable had a positive Cy of 0.5 at a velocity of 19 m/s in smooth flow. This 

positive value was eliminated almost completely by the turbulence with the exception of a small 

region with Cy ≈ 0.2 at 8 m/s.

Figure 39. Photo. Cable model at 60-degree inclination and 0-degree spring rotation in 

turbulent flow.

44
Figure 40. Graph. Amplitude of motion in sway and end-to-end sway at cable rotation of

-90 degrees and inclined at 60 degrees with a helical fillet in smooth and turbulent flow.

Figure 41. Graph. Mean force coefficients at cable rotation of -90 degrees and inclined at 

60 degrees with a helical fillet in smooth and turbulent flow.

45
Figure 42. Graph. Amplitude of motion in sway and end-to-end sway at cable rotation of

-90 degrees and inclined at 60 degrees without a helical fillet in smooth and turbulent flow.

Figure 43. Graph. Mean force coefficients at cable rotation of -90 degrees and inclined at 

60 degrees without a helical fillet in smooth and turbulent flow.

INFLUENCE OF THE HELICAL FILLET

The helical fillet did not mitigate the vibration of the cable. Figure 40 and figure 42 show 

examples of the response of the cable for different conditions with and without the presence of 

the helical fillet, respectively. Figure 44 and figure 45 present the results associated with the 

effect of the presence of the helical fillet for cable rotated at -90 and 0 degrees in smooth flow 

and the effect of the helical fillet on the mean force coefficients observed for the case at 

0 degrees. Sinusoidal wind-induced vibrations were observed independent of the helical fillet. 

However, the amplitude of vibrations was in general lower when the fillet was in place, and the 

vibrations occurred at a higher wind speeds.

46
Figure 44. Graph. Amplitude of motion in sway and end-to-end sway for cable rotated at 

-90 and 0 degrees and inclined at 60 degrees in smooth flow with and without a helical 

fillet.

Figure 45. Graph. Mean force coefficients for cable rotated at 0 degrees and inclined at 

60 degrees in smooth flow with and without helical fillet.

The helical fillet shifted the critical Reynolds number regime to lower wind speeds similar to the 

effect associated with an increase of surface roughness. The rate of change of both the alongwind and across-wind mean force coefficients with Reynolds number was found to be lower with 

the helical fillet in place. Nevertheless, large vibrations were observed for the cable model 

inclined at 60 degrees with the helical fillet in smooth flow over a range of Reynolds number

where the coefficients did not change rapidly with wind speed. This is opposite to observations 

made during previous studies on the same model, where the change of the coefficients with 

Reynolds number was identified as the primary cause of the cable vibrations, in particular when 

the static coefficient curves reached a point of inflection as a function of Reynolds number, as 

clearly demonstrated by Andersen.

(7) It can thus be inferred that the local increase of surface 

47
roughness of the cable model due to the presence of the helical fillet had an influence on the 

excitation mechanism.

INFLUENCE OF MOTION ON THE MEAN AERODYNAMIC FORCE 

COEFFICIENTS

For selected configurations, it was possible to compare the mean force coefficients for the model 

locked in a static position to the coefficients when the model was free to respond to wind 

excitation using the spring suspension system. In general, for cable rotation angles of -92, -90,

and -88 degrees, the mean Cy proved to be similar between the stationary model case and the 

moving model case for the model with a helical fillet in smooth flow at 60 degrees inclination. 

However, locally, the four different rings did not show similar distributions of surface pressures 

for the two cases. Figure 46 and figure 47 show the mean surface pressure distribution at 

approximately 11.5 m/s for the cable rotated at -90 degrees and in a static position and for the 

cable in motion (dynamic). The pressure around the four rings was not evenly distributed and 

that more surface pressure taps would be required to accurately predict the mean forces acting on 

the entire cable length. For the static cable, the negative lobe of pressure due to the laminar 

separation bubbles was active over a larger surface of the cable, and the magnitude was larger 

than for the case when the cable was in motion.

Figure 46. Illustration. Distribution of surface pressure coefficient for the four rings with 

the cable in a static position (run 81).

48
Figure 47. Illustration. Distribution of surface pressure coefficient for the four rings with 

the cable in motion (run 122).

Tests with the cable in a static position were also conducted to identify possible galloping using 

the Den Hartog criterion. Figure 48 shows the mean Cx and Cy calculated from the surface 

pressure distribution on the four rings as a function of wind angle for the cable in static position 

and as a function of wind speed for the cable in motion. A negative slope of Cy with cable 

rotation was depicted between -94 and -92 degrees. However, this slope was not large enough to 

satisfy the Den Hartog criterion.

49
Figure 48. Graph. Mean force coefficients as a function of cable rotation for the static cable 

and as a function of wind speed for cable in motion.

INFLUENCE OF THE END CONDITIONS AT THE TOP OF THE CABLE MODEL

Tests were conducted with the cable in a static position with the gap at the top of the cable open 

and sealed. The gap is necessary to allow the cable to move freely during dynamic test. The size 

of the opening was selected based on the amplitude of vibration expected. However, this opening 

has an impact on the flow around the cable near the roof of the test section. To evaluate the 

effect of this opening on the mean force coefficients as calculated from the surface pressure 

distributions, the gap was left opened and then sealed, as illustrated in figure 12 and figure 13. 

Results presented in figure 174 and figure 175 in appendix B indicate that Cx and Cy were not 

affected by the end conditions of the model, at least not for the region of the cable where the 

pressure rings were located.

It should be noted that the four rings of pressure taps are far (11 to 17 cable diameters) from the 

top of the cable where the opening is located. Therefore, the surface pressure distribution at those 

four locations might not have captured the difference in the flow field that is locally affected at 

the top of the cable. Adding rings of pressure taps along the main axis of the cable would have 

helped to better estimate the mean force coefficient acting on the entire cable length. The 

verification of the influence of the end conditions was carried out in smooth flow for the cable 

model without helical fillet at an inclination of 60 degrees corresponding to the test conditions of 

the 2001 and 2008 experiments. (See references 4–7.)

50
RELATIONSHIP BETWEEN THE SURFACE PRESSURES AND THE WAKE 

SIGNATURE

A TFI Cobra Probe was installed directly downwind of pressure ring 3 to look for any correlation 

between the surface pressure and the wake characteristics. The position of the TFI Cobra Probe 

in relation to the model is crucial to capture wake characteristics associated with flow 

phenomena of the separated shear layers. The appropriate position would be a function of 

Reynolds number, the trajectory of the motion, and the cable rotation. In light of all the possible 

ideal probe positions and time limitations, it was decided to set the probe at a fixed position 

during the entire test. The position was considered appropriate to capture the flow shed in the 

wake: wake of ring 3, on the tip of the probe 403 mm (2.5 cable diameters) behind the cable 

model, and 5 mm inboard of the model edge on the port side (south side). Figure 49 shows the 

TFI Cobra Probe as positioned relative to the model.

Figure 49. Photo. TFI Cobra Probe placed in the wake of the cable model directly behind 

ring 3 of pressure taps.

Spectral analysis of selected pressure ports located on the port side of the cable along with a 

spectral analysis of the signal captured by the probe in the wake have indicated that a 

relationship can be established for some cases. Figure 50 presents the spectrum of the 

longitudinal wind speed measured with the TFI Cobra Probe and the spectrum of pressure port 

30 on ring 3 for a wind speed of approximately 24 m/s (run 178). These spectrums were obtained 

from a dynamic test featuring the model with a helical fillet in smooth flow. Both spectrums

showed a peak of energy at about 1.5 and 2.1 Hz, corresponding to the frequencies of oscillation 

of the cable model. A detailed study of the relationships between unsteady pressure fluctuations, 

the cable motion, and fluctuations in the wake is beyond the scope of the present report.

51
Figure 50. Graph. Spectrum of the longitudinal flow velocity fluctuations located in the 

wake of the model and spectrum of the surface pressure signal of port 30 on ring 3 with a 

wind speed of 24 m/s.

GENERAL CHARACTERISTICS OF MEAN FORCE COEFFICIENTS WITH 

REYNOLDS NUMBER

The mean Cy was calculated for each configuration of the cable using two methods. The first 

method is based on the overall mean displacement of the cable measured with the lasers, which 

was converted into the aerodynamic force necessary to obtain the measured mean displacement 

using the stiffness of the dynamic rig in the direction of the motion. The force was then divided 

by the mean dynamic pressure in the test section and by the diameter and length of the cable 

corresponding to the frontal area of the model. This method is identical to the method put in 

place by Andersen et al. and Andersen for analysis of the data from the 2001 and 2008 

experiments.(6,7) The second method is based directly on the surface pressure measurements at 

four locations along the main axis of the cable with a total of 32 pressure ports for each of the 

four rings of taps. Integration of the mean surface pressure measurements provided the local 

aerodynamic forces perpendicular to the main axis of the cable and normalized by the dynamic 

pressure, the cable diameter and a cable length of 1 m to provide Cy and Cx. The force 

coefficients at the four locations along the main axis of the cable were then averaged to provide 

the mean Cy and Cx.

It could be argued that both techniques used to calculate the mean force coefficient for the entire 

cable are not fully representative of the mean aerodynamic forces. The first method assumes that 

the cable is moving only in one mode with one given frequency and that the mean force acts at 

52
mid-length of the cable with the wind speed being constant along the entire length of the cable. 

Observations of the cable motion have indicated that these assumptions were not fully true. The 

second method assumes that the pressure distributions at other locations along the main axis of 

the cable are similar to the pressure distribution obtained from the four measurement locations 

along the cable axis and that the mean wind speed is constant along the entire length of the cable. 

Given the measured deviations from the mean diameter reported earlier (See “General” section 

in chapter 4) and the presence of the helical fillet, it is clear that these assumptions are also not 

true. However, it is believed that a more representative prediction of mean aerodynamic force 

coefficients on the cable model could be given by the average of the force coefficients obtained 

from both sets of measurements. The results from surface pressure measurements have the 

tendency to underestimate the aerodynamic forces since the part related to friction is not 

considered, while the forces calculated from the measured overall displacements and the 

frequency of oscillations can represent an overestimation of the forces.

The force coefficients were calculated using both methods for each configuration of the cable 

model. It was assumed at first that a rotation of the cable along its main axis should not be a 

factor that affected the mean aerodynamic force coefficients. However, during the wind-tunnel 

tests, it was observed that the response of the cable for different cable rotations along its main 

axis differed greatly from angle to angle. Variations in terms of amplitude of motion of the cable, 

wind speed at which vibration occurred, and modes of vibration that were excited were observed 

for the different cable rotations tested. Variations of the mean force coefficients were also 

observed.

Figure 51 shows Cx and Cy calculated from measured displacements (top), from surface pressure 

measurements (center), and from the average of both methods (bottom) for the 17 different cable 

rotation angles tested for the cable inclined at 60 degrees in smooth flow and with the helical 

fillet. The red line on the bottom graphs represents a least-square fit of the mean force coefficient 

versus Reynolds number for the 17 configurations combined together. The red lines should be 

taken as the best representation of the cross-sectional force coefficients of the cable for the 

configuration mentioned previously. The same analysis was carried out and is presented in 

figure 52 through figure 55, where coefficients are calculated from mean displacement (top), 

integration of surface pressure (center), and mean of both methods (bottom).

53
Note: Coefficients are calculated from mean displacement in the top row, from integration of surface pressure in 

the center row, and from mean of both methods in the bottom row.

Figure 51. Graph. Variations of Cx and Cy with wind speed for 17 cable rotations with cable 

inclined at 60 degrees in smooth flow and with the helical fillet. 

54
Note: Coefficients are calculated from mean displacement in the top row, from integration of surface pressure in 

the center row, and from mean of both methods in the bottom row.

Figure 52. Graph. Variations of Cx and Cy with wind speed for five cable rotations with

cable inclined at 60 degrees in turbulent flow and with the helical fillet.

55
Note: Coefficients are calculated from mean displacement in the top row, from integration of surface pressure in 

the center row, and from mean of both methods in the bottom row.

Figure 53. Graph. Variations of Cx and Cy with wind speed for six cable rotations with

cable inclined at 60 degrees in turbulent flow and without the helical fillet.

56
Note: Coefficients are calculated from mean displacement in the top row, from integration of surface pressure in 

the center row, and from mean of both methods in the bottom row.

Figure 54. Graph. Variations of Cx and Cy with wind speed for seven cable rotations with

cable inclined at 60 degrees in smooth flow and without the helical fillet.

57
Note: Coefficients are calculated from mean displacement in the top row, from integration of surface pressure in 

the center row, and from mean of both methods in the bottom row.

Figure 55. Graph. Variations of Cx and Cy with wind speed for five cable rotations with

cable inclined at 45 degrees in smooth flow and with the helical fillet.

REPEATABILITY OF THE TESTS

The test program included verifications of the degree of repeatability that could be achieved 

during the experimental investigation. Selected static and dynamic tests were systematically 

repeated for conditions as close as possible to the original conditions.

For the static tests, comparisons of the mean cross-sectional force coefficients for the four rings 

of pressure taps between two identical runs showed excellent repeatability. The differences 

between the curves of Cx and Cy with Reynolds number were found to be negligible for the cable 

in smooth flow with helical fillet. Note that each coefficient was based on the integration of 

90-s time histories of 32 pressure taps composed of 28,000 points that were time averaged to 

obtain a single value.

58
For the dynamic tests, the following four factors had a significant influence on repeatability:

• The wind conditions outdoors.

• The level of structural damping.

• The procedure used by the operator to increment the wind speed of the wind tunnel.

• The surface conditions of the model.

As illustrated in the “Influence of Structural Damping” section earlier in this chapter, the wind 

conditions outside the wind tunnel were a significant factor to consider when tests were repeated. 

On windy days, the turbulence of the flow in the test section increased, and low frequency 

modulation of the wind speed were observed. The wind tunnel operator had to be vigilant in 

setting up the mean wind speed, deviating in some cases with the standard procedure and the 

desired increments.

It was observed early in the test program that during long tests with large amplitude of vibration, 

elements of the dynamic rig had a tendency to loosen up, increasing the friction between moving 

parts and therefore the structural damping. These elements were identified and systematically 

verified afterwards to keep the structural damping to a constant level.

Given the dependency of the mean wind speed inside the test section to the outdoor conditions, 

the wind tunnel operator had to set the wind speed manually based on a live display of the 

wind velocity in the test section. Once the speed was set, data were collected for 90 s, and the 

operator increased the speed to the next desired wind speed and repeated the process for 

16–17 increments. Care was taken never to reduce the wind speed if the desired wind speed was 

overshot. It was observed in some occasions that the model had a tendency to behave differently 

if the wind speed was increased rapidly or slowly. Given the important inertia of the model 

(407 kg) and the low frequency of oscillations (1.4 Hz), it is possible that oscillations present at 

low wind speed would carry to higher wind speeds. The excitation of the end-to-end modes in 

some instances complicated things as well. Therefore, the difficulty for the operator to adjust the 

mean wind speed in windy days could have combined with the increase of turbulence in the test 

section to affect the repeatability of the experiments.

In the 2001 and 2008 experiments, carried out in early spring, bugs (e.g., mosquitos, black flies, 

etc.) were found at several occasions on the windward surface of the model, significantly 

affecting the surface roughness. (See references 4–7.) The present investigation was carried 

out later in the spring than the previous experiments. As a result, bugs were observed only 

occasionally and were systematically removed from the surface of the model during 

model inspection.

When all four factors were controlled and the dynamic tests were repeated back to back, the 

variation of the model response with wind speed is repeatable. If a particular test that had large 

vibration amplitude needed to be repeated for further analysis, it was possible to reproduce the 

same amplitude of vibrations in the majority of the cases.

59
Figure 56 and figure 57 compare results of two sets of tests that were repeated. The first case 

involved static tests where mean force coefficients were compared (runs 81 and 94) and the 

second case involved dynamic tests where a run that was aborted midway was reran shortly after 

(runs 239 and 244). The agreement for both cases was excellent, as seen by the overlapping data 

in the figures.

Figure 56. Graph. Mean Cx and Cy calculated from the integration of surface pressure 

measurements for two runs with cable inclined at 60 degrees and rotated at -90 degrees in 

smooth flow and with helical fillet.

60
Figure 57. Graph. Response of the cable for two consecutive runs for the cable inclined at 

60 degrees and rotated at 2 degrees in smooth flow and without the helical fillet.

Figure 58 shows the results of four runs carried out for the exact same conditions without 

manipulation of the model. The first run was carried out rapidly with a sampling time of 10 s, the 

second run was carried out slowly with a sampling time of 90 s, the third run was done for only 

the low speed range up to 22 m/s, and the fourth run focused only on a peak in the amplitude 

around 22 m/s. The large peak observed in the first run had a lower amplitude during the second 

run. The peak was reproduced during the fourth run where the operator rapidly increased or 

decreased the wind speed to the desired value.

61
Figure 58. Graph. Amplitude of motion in sway for four consecutive runs for the cable 

inclined at 60 degrees and rotated at -88 degrees without the helical fillet and in smooth 

flow.

MECHANISMS CAUSING THE VIBRATIONS

At the time of the initiation of this experimental investigation, the phenomenon referred to 

as dry-inclined cable galloping could be defined as follows: wind-induced vibrations of stay 

cables for wind speed ranging from 4 to 40 m/s in dry conditions; sustained vibrations, mostly 

sinusoidal, mostly across-wind; self-limited in amplitude or divergent; and sensitive to 

fluctuations of the mean wind speed. It is different than buffeting due to turbulence; galloping 

due to the impinging wake of another structural element; parametric excitation; and galloping 

due to ice-accretion or other surface contamination.

The mechanisms involved for dry-inclined cable galloping include the following:

• Quasi-steady aerodynamic instability: The excitation of the cable is linked with the 

observation that the combination of the cable diameter and the wind speed range coincide 

with the critical Reynolds number regime for bi-dimensional circular cylinders. In this 

regime, several sub-regimes exist, associated with the state of the boundary layers at the 

surface of the stay cables. The different sub-regimes have different aerodynamic 

characteristics such as different along-wind and across-wind static force coefficients. The 

passage from one sub-regime to another due to a small change of apparent wind speed or 

direction can induce a sudden change of static force coefficients. The rate of change of 

the static coefficients with Reynolds number and cable wind angle could make it so that 

the Den Hartog instability criterion is satisfied, and the stay cable experiences galloping. 

It could also be that the aerodynamics of the stay cable fluctuate from one sub-regime to 

the next due to motion, fluctuating mean wind speed, and/or change of direction, 

generating fluctuating forces and causing vibrations. Finally, the rate of change of the 

62
static coefficients with Reynolds number could make it so that the aerodynamic damping 

in one of the modes of vibration becomes negative causing a growth of the vibrations.

• High-reduced velocity vortex shedding: The excitation of the cable is linked with the 

axial flow and axial vortices that develop along the leeward surface of the inclined stay 

cable. The low-reduced velocity vortex shedding process known as von Kármán vortex 

shedding interferes with the axial flow and axial vortices that are travelling slightly 

downward along the length of the cable, moving farther away from the cable in the 

process until they are finally released. Vortex cells are formed, and the low-reduced 

velocity vortex shedding process gets synchronized with the axial vortex shedding 

process, creating the shedding of entire vortex cells. The process is influenced by many 

factors and is not necessarily regular and not necessarily coherent along the length of the 

cable. The excitation occurs at low frequency, 20–30 times lower than the regular vortexshedding frequency, hence the name “high-reduced velocity vortex shedding.”

These two instability mechanisms are intertwined for inclined stay cables. For example, the 

variations of the state of the boundary layer due to Reynolds number effects will affect the 

generation of the axial vortices, affecting the shedding frequency and the wind speed at which 

the vibration occurs. The vortex shedding and associated motion will affect the apparent wind 

speed and direction, defining the critical Reynolds number sub-regime experienced by the stay 

cable and affecting the cross-sectional force coefficients.

In light of the experiments carried out in the framework of this investigation, it can be concluded 

that the vibrations observed for the cable model with a helical fillet in smooth and turbulent flow 

generally matched the earlier definition of dry-inclined cable galloping with some exceptions. 

The vibrations were mostly sinusoidal, across-wind, self-limited in amplitude, influenced by 

slow fluctuations of the mean wind speed, and affected by the level of structural damping. Peaks 

at lower wind speeds were observed and disappeared with an increase of speed similar to a 

typical vortex shedding process or due to a change of Reynolds number sub-regime.

For the tests in smooth flow with the helical fillet for several cable angle rotations, the maximum 

amplitude occurred at the highest wind speed attainable in the wind tunnel—36 m/s. At this 

Reynolds number, the cable model had cross-sectional force coefficients varying slowly with 

wind speed in contrast to what would be expected from dry-inclined cable galloping. Tests were 

carried out to define if the Den Hartog criterion was met due to variations of the static 

coefficients with cable angle rotation. This was not the case even though a negative slope of the 

across-wind coefficients with cable rotation was depicted. It was not possible to verify if it was a 

high-reduced vortex shedding peak given that the maximum speed of the wind tunnel was 

reached.

Tests in turbulent flow for the same conditions have shown that the peak occurred at lower wind 

speed (i.e., at a lower Reynolds number) and that the vibrations switched to a higher frequency 

mode with end-to-end sway when wind speed was increased. It is possible that a similar behavior 

would have been observed in smooth flow if it had been possible to increase the wind speed past

the observed peak.

63
For other cases, sinusoidal vibrations with constant amplitude were observed, and the amplitude 

increased when wind speed was increased. This was the case for a large number of wind speed 

increments corresponding to a range of 10 to 12 m/s. At higher speeds, the vibrations in the sway 

mode subsided, and vibrations in the end-to-end sway mode occurred. Given the large range of 

wind speeds covered, this behavior does not match 100 percent with the expected general 

behavior of dry-inclined cable galloping.

Nevertheless, the fact that stay cables operate in the critical Reynolds number regime with 

or without the helical fillet and in smooth or turbulent flow makes the description of the 

phenomenon more complex. In this regime, the boundary layers near the surface of the stay 

cable experience a transition from laminar to turbulent flow where separation and sometimes 

reattachment followed by separation occur. These processes are known to be unstable and can 

lead to unstable behavior. Boundary layer transition from laminar to turbulent at the surface of a 

circular cylinder is an instability phenomenon that is sensitive to components such as the microstructure of the surface, geometric asymmetry, flow turbulence, noise, and small motion. It 

amplifies the effects of these external factors. A deviation of 1 percent of the mean diameter that 

normally might have been negligible in different conditions becomes a dominating factor in the 

critical Reynolds number regime. Adding this to the complexity of the aerodynamics of circular 

cylinders inclined to the flow has proved to be a challenging instability problem to describe 

and control.

64
CHAPTER 5: CONCLUSIONS

The aerodynamics of a stay cable model fitted with a helical fillet and inclined to the oncoming 

flow were studied to evaluate the effect of adding a helical fillet at the surface of a stay cable in 

relation to its response to strong winds. A helical fillet with a double helix representative of what 

can be found on stay cables in Europe and North America was affixed to the surface of the 

HDPE tube of an existing cable model. The helical fillet had a rectangular cross section 2.3 mm 

high and 2.4 mm wide, a pitch equivalent to 3.2 cable diameters, and a helix angle of 45 degrees.

The experiments revealed that a stay cable with a representative surface roughness, crosssectional shape, and helical fillet inclined at 60 degrees to the flow can experience wind-induced 

vibrations with large amplitudes in smooth or turbulent flow for a low level of structural 

damping. The oscillations observed appeared to be self-limited in amplitude and could be 

mitigated with an increase of structural damping equivalent to a Scruton number of 5.1. The 

cable model with the helical fillet experienced a drag crisis almost as pronounced as for the 

smooth cable but at a lower Reynolds number range.

The experiments revealed also that the aerodynamic forces at the source of the vibrations were 

highly sensitive to a rotation of the cable model on its axis. Measurements of the external 

diameter of the smooth cable model have shown a maximum eccentricity equivalent to 1 percent

of the mean diameter, which appeared to be sufficient to influence the aerodynamics of the cable 

model even with the helical fillet in place. Such deviation from the mean cable diameter was 

deemed representative of field conditions. The trajectory of the cable motion in relation to the 

prevailing wind direction was also found to be a parameter of importance in the study of cable 

behavior and stability. During the previous studies on inclined cable galloping, it had not been 

possible to reach any conclusions on this aspect since the cable-wind plane and rotation of the 

cable on its axis could not be evaluated separately.

For a stay cable inclined at 45 degrees with a helical fillet, no large vibrations were observed for 

the range of wind speed investigated, 4 to 36 m/s, for several experimental conditions including 

spring-plane rotation and rotation of the cable on its axis. The rate of change of the mean 

aerodynamic force coefficients with wind speeds for a model inclination of 45 degrees were 

found to be lower than for the 60-degree inclination cases.

Complementary tests on the cable model without the helical fillet in smooth and turbulent flow at 

an inclination of 60 degrees revealed large vibrations in accordance with the results of previous 

studies on the same cable model. The vibrations were equivalent and sometimes larger in 

amplitude than what was previously reported and did not happen at the same wind speeds. This 

emphasized the importance of the shape of the polyethylene tube covering the stay cable, a local 

1 percent deviation from the mean diameter, which was sufficient to amplify the wind excitation.

65

67

APPENDIX A. DETAILED LIST OF RUNS AND EXPERIMENTAL CONDITIONS

Table 6. Description of all the runs completed during the 2011 wind tunnel test.

Day Tare

Run

No.

No. 

of 

Pts

Inclination

(Degree)

Spring 

Rotation

(Degreea)

Cable 

Rotation

(Degreea) Case Description

Freq.

Sway

(Hz)

Freq.

Heave

(Hz)

Freq.

Ratio

Damping

Sway

(Percent)

Damping

Heave

(Percent)

Sc

Sway

Sc

Heave Comments

5/6 24 4 60 0 0 Dynamic Damping trace 1.39 1.39 1.0 0.08 0.10 1.6 2.1 pt1: sway; pt2: heave; pt3: endto-end sway; pt4: end-to-end 

heave

5/6 25 27 19 60 0 0 Dynamic Increasing speed sweep pt1–19: speed sweep

5/6 25 28 20 60 0 0 Dynamic Decreasing speed sweep pt1–20: speed sweep

5/9 31 32 15 60 0 0 Static Increasing speed sweep pt1–15: speed sweep

5/9 34 35 15 60 0 0 Static Decreasing speed sweep pt1–15: speed sweep

5/9 36 37 12 60 0 27.7 Static Increasing speed sweep pt1–12: speed sweep

5/10 38 39 15 60 0 -13.8 Static Increasing speed sweep pt1–15: speed sweep

5/10 40 41 15 60 0 13.8 Static Increasing speed sweep pt1–15: speed sweep

5/10 42 2 60 0 -13.8 Dynamic Damping trace 1.39 1.39 1.00 0.08 0.10 1.6 2.1 pt1: sway; pt2: heave

5/10 43 44 17 60 0 -13.8 Dynamic Increasing speed sweep pt1–17: speed sweep

5/10 45 46 17 60 0 -13.8 Dynamic Increasing speed sweep pt1–17: speed sweep; repeat of 

run 44

5/10 45 47 5 60 0 -13.8 Dynamic Forced oscillations pt1: 12m/s; pt2: 18m/s; pt3:

24m/s; pt4: 30m/s; pt5: 34m/s

5/11 48 49 17 60 0 -30 Dynamic Increasing speed sweep pt1–17: speed sweep

5/11 48 50 4 60 0 -30 Dynamic Forced oscillations pt1: 24m/s; pt2: 26m/s; pt3:

28m/s; pt4: 34m/s

5/11 51 52 17 60 0 -40 Dynamic Increasing speed sweep pt1–17: speed sweep

5/11 51 53 3 60 0 -40 Dynamic Forced oscillations pt1: 24m/s; pt2: 28m/s; pt3:

34m/s

5/11 55 56 17 60 0 -50 Dynamic Increasing speed sweep pt1–7: speed sweep

5/11 55 58 2 60 0 -50 Dynamic Forced oscillations pt1: 24m/s; pt2: 28m/s

5/11 59 60 17 60 0 -60 Dynamic Increasing speed sweep pt1–17: speed sweep

5/11 59 61 6 60 0 -60 Dynamic Forced oscillations pt1: 14m/s; pt2: 22m/s; pt3:

22m/s; pt4: 30m/s; pt5/6: 36m/s

5/12 62 63 17 60 0 -75 Dynamic Increasing speed sweep pt1–17: speed sweep

5/12 62 64 3 60 0 -75 Dynamic Forced oscillations pt1: 16m/s; pt2: 22m/s; pt3:

36m/s

5/12 65 66 19 60 0 -90 Dynamic Increasing speed sweep pt1–19: speed sweep

5/12 65 67 17 60 0 -90 Dynamic Decreasing speed sweep pt1–17: speed sweep
68

Day Tare

Run

No.

No. 

of 

Pts

Inclination

(Degree)

Spring 

Rotation

(Degreea)

Cable 

Rotation

(Degreea) Case Description

Freq.

Sway

(Hz)

Freq.

Heave

(Hz)

Freq.

Ratio

Damping

Sway

(Percent)

Damping

Heave

(Percent)

Sc

Sway

Sc

Heave Comments

5/12 68 69 17 60 0 5 Dynamic Increasing speed sweep pt1–17: speed sweep

5/12 70 71 17 60 0 65 Dynamic Increasing speed sweep pt1–17: speed sweep

5/13 72 73 18 60 0 50 Dynamic Increasing speed sweep pt1–18: speed sweep

5/13 74 75 20 60 0 -90 Dynamic Increasing speed sweep pt1–20: speed sweep, repeat 

run 66

5/13 74 76 2 60 0 -90 Dynamic Aerodynamic damping 

test

pt1–2: aerodynamic damping at 

32m/s

5/13 74 79 5 60 0 -90 Dynamic Aerodynamic damping 

test

pt1: 20m/s; pt2:data taken from 

20–22m/s; pt3: data taken while 

increasing speed from 20 to

22m/s; pt4: aero damping at 

32m/s

5/13 80 81 16 60 0 -90 Static Increasing speed sweep pt1–16: speed sweep

5/13 84 85 15 60 0 -86 Static Increasing speed sweep pt1–15: speed sweep

5/16 87 88 15 60 0 -88 Static Increasing speed sweep pt1–15: speed sweep

5/16 89 90 15 60 0 -92 Static Increasing speed sweep pt1–15: speed sweep

5/16 91 92 15 60 0 -94 Static Increasing speed sweep pt1–15: speed sweep

5/16 93 94 15 60 0 -90 Static Increasing speed sweep pt1–15: speed sweep, repeat run

81 (helical fillet lifted because of 

cold weather)

5/16 96 2 60 0 -90 Dynamic Damping trace 1.39 1.39 1.00 pt1: sway; pt2: heave

5/16 97 1 60 0 -90 Dynamic Damping trace 1.39 pt1: sway

5/16 98 1 60 0 -90 Dynamic Damping trace 1.4 pt1: sway

5/16 99 1 60 0 -90 Dynamic Damping trace 1.4 pt1: sway

5/16 100 3 60 0 -90 Dynamic Damping trace 1.4 1.4 1.00 0.15 0.40 3.0 8.1 pt1: sway; pt2: heave

5/17 100 101 20 60 0 -90 Dynamic Increasing speed sweep pt1–20: speed sweep, two elastic 

bands broke during pt8

5/17 100 102 2 60 0 -90 Dynamic Aerodynamic damping 

test

pt1–2: aerodynamic damping at 

36m/s

5/17 103 2 60 0 -90 Dynamic Damping trace 1.4 1.4 1.00 pt1: sway; pt2: heave

5/17 104 1 60 0 -90 Dynamic Damping trace 1.4 pt1: sway

5/17 105 1 60 0 -90 Dynamic Damping trace 1.4 pt1: heave

5/17 106 4 60 0 -90 Dynamic Damping trace 1.4 1.4 1.00 0.15 0.15 3.0 3.0 pt3: sway; pt4: heave, medium

damping

5/17 107 108 18 60 0 -90 Dynamic Increasing speed sweep pt1–18: speed sweep

5/17 109 2 60 0 -90 Dynamic Damping trace 1.4 1.4 1.00 pt1: sway; pt2: heave

5/17 110 2 60 0 -90 Dynamic Damping trace 1.4 1.4 1.00 pt1: sway; pt2: heave
69

Day Tare

Run

No.

No. 

of 

Pts

Inclination

(Degree)

Spring 

Rotation

(Degreea)

Cable 

Rotation

(Degreea) Case Description

Freq.

Sway

(Hz)

Freq.

Heave

(Hz)

Freq.

Ratio

Damping

Sway

(Percent)

Damping

Heave

(Percent)

Sc

Sway

Sc

Heave Comments

5/17 111 1 60 0 -90 Dynamic Damping trace 1.39 pt1: sway

5/17 112 1 60 0 -90 Dynamic Damping trace 1.39 pt1: sway

5/17 113 1 60 0 -90 Dynamic Damping trace 1.4 pt1: heave

5/17 114 2 60 0 -90 Dynamic Damping trace 1.42 pt1: heave

5/17 115 1 60 0 -90 Dynamic Damping trace 1.4 pt1: sway

5/18 116 2 60 0 -90 Dynamic Damping trace 1.4 1.42 0.99 0.25 0.25 5.1 5.1 pt1: sway; pt2: heave, high

damping

5/18 117 118 23 60 0 -90 Dynamic Increasing speed sweep pt1–23: speed sweep

5/18 119 2 60 0 -90 Dynamic Damping trace 1.4 1.42 0.99 pt1: sway; pt2: heave

5/18 120 2 60 0 -90 Dynamic Damping trace 1.39 1.4 0.99 0.08 0.15 1.0 3.1 pt1: sway; pt2: heave, low

damping

5/18 121 122 24 60 0 -90 Dynamic Increasing speed sweep pt1–24: speed sweep

5/18 121 123 12 60 0 -90 Dynamic Decreasing speed sweep pt1–12: speed sweep

End of Phase I and Start of Phase II

5/19 124 125 13 60 0 -88 Dynamic Increasing speed sweep pt1–13: speed sweep

5/19 126 2 60 0 -88 Dynamic Damping trace 1.39 1.39 1.00 pt1: sway; pt2: heave

5/19 128 8 60 -54.7 -90 Dynamic Damping trace 1.4 0.12 2.5 pt1: sway

5/19 129 1 60 -54.7 -90 Dynamic Damping trace 1.42 0.20 4.2 pt1: heave

5/19 130 131 18 60 -54.7 -90 Dynamic Increasing speed sweep pt1–18: speed sweep

Change to 45-Degree Inclination

5/24 133 3 45 0 -90 Dynamic Damping trace 1.42 1.37 1.04 0.12 0.10 2.4 2.1 pt2: sway; pt3: heave

5/24 135 136 15 45 0 -90 Dynamic Increasing speed sweep pt1–15: speed sweep

5/25 137 137 21 45 0 0 Dynamic Increasing speed sweep pt1–21: speed sweep

5/25 138 2 45 0 90 Dynamic Damping trace 1.42 1.39 1.02 0.12 0.08 2.4 1.6 pt1: sway; pt2: heave

5/25 139 140 17 45 0 90 Dynamic Increasing speed sweep pt1–17: speed sweep

5/25 141 142 17 45 0 23 Dynamic Increasing speed sweep pt1–17: speed sweep

5/25 143 144 18 45 0 -25 Dynamic Increasing speed sweep pt1–18: speed sweep

5/27 147 2 45 -54.7 -25 Dynamic Damping trace 1.42 1.43 0.99 0.09 0.07 1.8 1.4 pt1: heave; pt2: sway

5/27 148 149 24 45 -54.7 -25 Dynamic Increasing speed sweep pt1–24: speed sweep, beating

5/27 150 1 45 -54.7 0 Dynamic Damping trace 1.43 0.05 1.0 pt1: heave

5/27 151 152 18 45 -54.7 0 Dynamic Increasing speed sweep pt1–18: speed sweep, beating

5/27 153 2 45 -45 -25 Dynamic Damping trace 1.42 1.43 0.99 0.16 0.06 3.3 1.2 pt1: heave; pt2:sway

5/27 154 155 24 45 -45 -25 Dynamic Increasing speed sweep pt1–23: speed sweep; pt24:

deceleration, beating

5/30 157 3 45 -12.5 -25 Dynamic Damping trace 1.45 1.39 1.04 0.14 0.10 3.0 2.1 pt2: heave; pt3: sway
70

Day Tare

Run

No.

No. 

of 

Pts

Inclination

(Degree)

Spring 

Rotation

(Degreea)

Cable 

Rotation

(Degreea) Case Description

Freq.

Sway

(Hz)

Freq.

Heave

(Hz)

Freq.

Ratio

Damping

Sway

(Percent)

Damping

Heave

(Percent)

Sc

Sway

Sc

Heave Comments

5/30 158 159 21 45 -12.5 -25 Dynamic Increasing speed sweep pt1–23: speed sweep; pt24:

deceleration, beating

Change Back to 60-Degree Inclination

6/1 161 4 60 -12.5 -90 Dynamic Damping trace 1.43 1.39 1.01 0.10 0.14 2.2 3.0 pt3: sway; pt4: heave

6/1 162 163 24 60 -12.5 -90 Dynamic Increasing speed sweep pt1–23: speed sweep; pt24:

deceleration run, very windy

6/1 164 2 60 Damping trace pt1: sway; pt2: heave

6/7 165 2 60 Damping trace 1.43 1.39 1.03 0.09 0.10 2.0 2.2 pt1: sway; pt2: heave

6/7 166 167 31 60 -12.5 -90 Dynamic Increasing speed sweep pt1–29: speed sweep; pt30–31:

aerodynamic damping

6/7 Repeat of run 163

6/7 166 168 1 60 -12.5 -90 Dynamic Ramp down from max 

speed to 0 m/s

pt1: deceleration run

6/7 171 2 60 Damping trace pt1: sway

6/8 173 5 60 Damping trace 1.4 1.39 1.01 0.08 0.15 1.7 3.3 pt3: sway; pt4: heave

6/8 174 176 25 60 0 -92 Dynamic Increasing speed sweep pt1–22: speed sweep; pt23–24:

aerodynamic damping; pt25:

deceleration

6/8 177 178 16 60 0 -90 Dynamic Increasing speed sweep pt1–13: speed sweep; pt14–15:

aerodynamic damping

6/15 179 180 4 60 Turbulent flow 

characteristic

Position 1 of the ladders upstream 

of the cable

6/15 181 182 5 60 Turbulent flow 

characteristic

Position 2 of the ladders 

(167.64 cm further away from the 

cable)

6/15 183 184 4 60 Turbulent flow 

characteristic

Position 2 of the ladders, first

vertical measurement

6/15 185 186 4 60 Turbulent flow 

characteristic

Position 2 of the ladders, second

vertical measurement

6/15 187 188 4 60 Turbulent flow 

characteristic

Position 2 of the ladders, third

vertical measurement

6/16 189 190 4 60 Turbulent flow 

characteristic

Position 2 of the ladders, fourth

vertical measurement

6/16 191 192 12 60 Turbulent flow 

characteristic

Calibration of the test section in 

turbulent flow, speed sweep

6/16 193 194 5 60 Turbulent flow 

characteristic

Position 2 of the ladders, measure 

of flow for different lateral 

positions
71

Day Tare

Run

No.

No. 

of 

Pts

Inclination

(Degree)

Spring 

Rotation

(Degreea)

Cable 

Rotation

(Degreea) Case Description

Freq.

Sway

(Hz)

Freq.

Heave

(Hz)

Freq.

Ratio

Damping

Sway

(Percent)

Damping

Heave

(Percent)

Sc

Sway

Sc

Heave Comments

6/16 195 2 60 0 -90 Dynamic Damping trace 1.4 1.39 1.01 0.08 0.15 1.7 3.3 pt1: sway; pt2: heave

6/16 196 197 22 60 0 -90 Dynamic Increasing speed sweep, 

turbulent flow

pt1–19: speed sweep; pt20–21:

aerodynamic damping; pt22:

deceleration

6/16 198 199 24 60 0 -92 Dynamic Increasing speed sweep, 

turbulent flow

pt1–23: speed sweep; pt24:

aerodynamic damping, one

threaded rod broke after pt24

6/17 201 3 60 0 -88 Dynamic Damping trace 1.4 1.39 1.01 0.07 0.13 1.5 2.7 pt1: sway, pt2:heave

6/17 202 203 24 60 0 -88 Dynamic Increasing speed sweep, 

turbulent flow

pt1–21: speed sweep; pt22–23:

aerodynamic damping; pt24:

deceleration, new threaded rod

6/17 204 205 2 60 0 0 Dynamic Increasing speed sweep, 

turbulent flow

pt1: 0m/s; pt2: 4m/s

6/17 204 206 19 60 0 0 Dynamic Increasing speed sweep, 

turbulent flow

pt1–16: speed sweep; pt17–18:

aerodynamic damping; pt19:

deceleration

6/17 207 208 27 60 0 50 Dynamic Increasing speed sweep, 

turbulent flow

pt1–24: speed sweep; pt25–26:

aerodynamic damping; pt27:

deceleration

Removal of Helical Fillet

6/20 209 3 60 0 50 Dynamic Damping trace 1.4 1.39 1.01 0.07 0.15 1.5 3.2 pt1: sway; pt2: heave

6/20 210 211 20 60 0 50 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–17: speed sweep; pt16: lost 

laser heave top; pt18–19:

aerodynamic damping; pt17–20:

not good, the cable was touching 

the top opening of the wind 

tunnel and damped motion; pt20:

deceleration

6/20 212 2 60 0 0 Dynamic Damping trace 1.4 1.39 1.01 0.08 0.12 pt1: sway; pt2: heave

6/20 213 214 23 60 0 0 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–19: speed sweep; pt20–21:

aerodynamic damping; pt22:

deceleration; pt23: tare

6/22 215 216 31 60 0 -90 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–28: speed sweep; pt29–30:

aerodynamic damping; pt31:

deceleration

6/22 218 219 19 60 0 -88 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–16: speed sweep; pt17–18:

aerodynamic damping; pt19:

deceleration

6/22 220 2 60 0 -92 Dynamic Damping trace 1.4 1.39 1.01 0.09 0.11 1.9 2.3 pt1: sway; pt2: heave
72

Day Tare

Run

No.

No. 

of 

Pts

Inclination

(Degree)

Spring 

Rotation

(Degreea)

Cable 

Rotation

(Degreea) Case Description

Freq.

Sway

(Hz)

Freq.

Heave

(Hz)

Freq.

Ratio

Damping

Sway

(Percent)

Damping

Heave

(Percent)

Sc

Sway

Sc

Heave Comments

6/22 221 222 16 60 0 -92 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–15: speed sweep; pt16: data 

at 32m/s but one threaded rod 

broke after 38 s of data

6/22 223 2 60 0 -54.7 Dynamic Damping trace 1.4 1.39 1.01 0.08 0.13 1.7 2.8 pt1: sway; pt2: heave

6/22 224 225 19 60 0 -54.7 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–16: speed sweep; pt17–18:

aerodynamic damping; pt19:

deceleration

6/22 227 226 9 60 0 -54.7 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–8: speed sweep (from 6 to 

9.5 m/s); pt9: 0 m/s

Removal of Turbulent Flow Exposure

6/23 228 2 60 0 -54.7 Dynamic Damping trace 1.4 1.39 1.01 0.07 0.11 1.5 2.3 pt1: sway, pt2: heave

6/23 229 230 22 60 0 -54.7 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–19: speed sweep; pt20–21:

aerodynamic damping; pt22:

deceleration

6/23 232 234 20 60 0 0 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–18: speed sweep; pt19–20:

aerodynamic damping, one

threaded rod broke during the run

6/23 235 2 60 0 -2 Dynamic Damping trace 1.4 1.39 1.01 0.07 0.13 1.5 2.7 pt1: sway; pt2: heave

6/23 236 237 21 60 0 -2 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–18: speed sweep; pt19–20:

aerodynamic damping; pt21:

deceleration

6/23 238 239 12 60 0 2 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–11: speed sweep; pt12: one

threaded rod broke during the run

6/23 240 3 60 0 2 Dynamic Damping trace 1.42 1.39 1.02 0.07 0.13 1.5 2.8 pt1: sway; pt2: heave

6/24 241 244 14 60 0 2 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–11: speed sweep (run 239 

with a new rod); pt12–13: 

aerodynamic damping; pt14: 

deceleration

6/24 247 248 15 60 0 -93 Static Increasing speed sweep, 

turbulent flow, no helical

pt1–15: speed sweep

6/24 249 250 16 60 0 -93 Static Increasing speed sweep, 

turbulent flow, no helical

pt1–16: speed sweep, top gap 

sealed

6/24 252 253 22 60 0 -93 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–19: speed sweep; pt20–21:

aerodynamic damping; pt22:

deceleration

6/24 254 2 60 0 -90 Dynamic Damping trace 1.4 1.39 1.01 0.07 0.12 1.5 2.6 pt1: sway; pt2: heave
73

Day Tare

Run

No.

No. 

of 

Pts

Inclination

(Degree)

Spring 

Rotation

(Degreea)

Cable 

Rotation

(Degreea) Case Description

Freq.

Sway

(Hz)

Freq.

Heave

(Hz)

Freq.

Ratio

Damping

Sway

(Percent)

Damping

Heave

(Percent)

Sc

Sway

Sc

Heave Comments

6/24 254 255 23 60 0 -90 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt2–18: speed sweep; pt19–22:

aerodynamic damping; pt23:

deceleration (no data for pt1)

6/24 256 257 19 60 0 -88 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–18:speed sweep; pt19:

aerodynamic damping, only 10-s 

sampling time at 500 Hz

6/24 256 258 1 60 0 -88 Dynamic Aerodynamic damping pt1: aerodynamic damping

6/24 259 260 22 60 0 -88 Dynamic Speed sweep, increasing, 

turbulent flow, no helical

pt1–16: speed sweep; pt17–21:

aerodynamic damping; pt22:

deceleration, repeat run 257 with 

90-s sampling time at 2500 Hz

6/24 261 262 8 60 0 -88 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1–8: speed sweep, 12 to 22 m/s 

increase by 2 m/s

6/24 261 263 7 60 0 -88 Dynamic Increasing speed sweep, 

turbulent flow, no helical

pt1: ramp up to 20 m/s; pt2:

20 m/s; pt3: down to 8 m/s and

back to 20 m/s; pt4–21: 7 m/s;

pt5: 20 m/s; pt6: up to 36 m/s and

back to 20 m/s and take data a Negative degrees indicate clockwise direction.

Note: Blank cells indicate that no information is available.

75

APPENDIX B. SUMMARY OF RESULTS

Figure 59. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 27.
76

Figure 60. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 27.
77

Figure 61. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 28.
78

Figure 62. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 28.
79

Figure 63. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 32.
80

Figure 64. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 35.
81

Figure 65. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 37.
82

Figure 66. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 39.
83

Figure 67. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 41.
84

Figure 68. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 44.
85

Figure 69. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 44.
86

Figure 70. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 46.
87

Figure 71. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 46.
88

Figure 72. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 49.
89

Figure 73. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 49.
90

Figure 74. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 52.
91

Figure 75. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 52.
92

Figure 76. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 56.
93

Figure 77. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 56.
94

Figure 78. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 60.
95

Figure 79. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 60.
96

Figure 80. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 63.
97

Figure 81. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 63.
98

Figure 82. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 66.
99

Figure 83. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 66.
100

Figure 84. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 67.
101

Figure 85. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 67.
102

Figure 86. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 69.
103

Figure 87. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 69.
104

Figure 88. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 71.
105

Figure 89. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 71.
106

Figure 90. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 73.
107

Figure 91. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 73.
108

Figure 92. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 75.
109

Figure 93. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 75.
110

Figure 94. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 81.
111

Figure 95. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 85.
112

Figure 96. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 88.
113

Figure 97. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 90.
114

Figure 98. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 92.
115

Figure 99. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 94.
116

Figure 100. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 101.
117

Figure 101. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 101.
118

Figure 102. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 108.
119

Figure 103. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 108.
120

Figure 104. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 118.
121

Figure 105. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 118.
122

Figure 106. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 122.
123

Figure 107. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 122.
124

Figure 108. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 123.
125

Figure 109. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 123.
126

Figure 110. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 125.
127

Figure 111. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 125.
128

Figure 112. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 131.
129

Figure 113. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 131.
130

Figure 114. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 136.
131

Figure 115. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 136.
132

Figure 116. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 137.
133

Figure 117. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 137.
134

Figure 118. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 140.
135

Figure 119. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 140.
136

Figure 120. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 142.
137

Figure 121. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 142.
138

Figure 122. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 144.
139

Figure 123. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 144.
140

Figure 124. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 149.
141

Figure 125. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 149.
142

Figure 126. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 152.
143

Figure 127. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 152.
144

Figure 128. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 155.
145

Figure 129. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 155.
146

Figure 130. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 159.
147

Figure 131. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 159.
148

Figure 132. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 163.
149

Figure 133. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 163.
150

Figure 134. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 167.
151

Figure 135. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 167.
152

Figure 136. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 176.
153

Figure 137. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 176.
154

Figure 138. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 178.
155

Figure 139. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 178.
156

Figure 140. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 197.
157

Figure 141. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 197.
158

Figure 142. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 199.
159

Figure 143. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 199.
160

Figure 144. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 203.
161

Figure 145. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 203.
162

Figure 146. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 206.
163

Figure 147. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 206.
164

Figure 148. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 208.
165

Figure 149. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 208.
166

Figure 150. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 211.
167

Figure 151. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 211.
168

Figure 152. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 214.
169

Figure 153. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 214.
170

Figure 154. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 216.
171

Figure 155. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 216.
172

Figure 156. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 219.
173

Figure 157. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 219.
174

Figure 158. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 222.
175

Figure 159. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 222.
176

Figure 160. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 225.
177

Figure 161. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 225.
178

Figure 162. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 226.
179

Figure 163. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 226.
180

Figure 164. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 230.
181

Figure 165. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 230.
182

Figure 166. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 234.
183

Figure 167. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 234.
184

Figure 168. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 237.
185

Figure 169. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 237.
186

Figure 170. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 239.
187

Figure 171. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 239.
188

Figure 172. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 244.
189

Figure 173. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 244.
190

Figure 174. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 248.
191

Figure 175. Graph. Intensity of turbulence measured at the entrance of the test section and Cx and Cy calculated from surface 

pressure measurements as a function of Reynolds number and wind speed for run 250.
192

Figure 176. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 253.
193

Figure 177. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 253.
194

Figure 178. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 255.
195

Figure 179. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 255.
196

Figure 180. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 257.
197

Figure 181. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 257.
198

Figure 182. Graph. Response of the cable as a function of wind speed or Reynolds number as measured by the lasers, 

accelerometers, and surface pressures for run 260.
199

Figure 183. Graph. Mean displacement and peak factor from the laser, motion path at one wind speed, and intensity of 

turbulence measured at the entrance of the test section for run 260.
Figure 184. Graph. Damping traces and level for the sway and heave modes for the low 

damping level case.

200
Figure 185. Graph. Damping traces and level for the sway and heave modes for the 

medium damping case.

201
Figure 186. Graph. Damping traces and level for the sway and heave modes for the high 

damping level case.

202
ACKNOWLEDGEMENTS

The authors would like to thank Mr. Harold R. Bosch, manager of the Aerodynamics Laboratory 

and Wind Research Program at FHWA’s Turner-Fairbank Highway Research Center, for 

overseeing the first phase of the experiments in Ottawa, Canada. We would also like to express 

our appreciation to Professor Jasna B. Jakobsen of the University of Stavanger, Professor John 

Macdonald from the University of Bristol, and Dr. Stoyan Stoyanoff who provided expert advice 

and guidance for the planning and execution of the tests. Professor Jakobsen and Dr. Stoyanoff 

also oversaw part of the experiments of phases I and II at NRC-IAR.

203

REFERENCES

1. Post-Tensioning Institute. (2012). Recommendations for Stay Cable Design, Testing, and 

Installation, Sixth Edition, Post-Tensioning Institute, Farmington Hills, MI.

2. Flamand, O. and Gandemer, J. (1992). Effet Combiné du Vent et de la Pluie Sur Les Haubans 

du Pont de Normandie, No. EN-SC 92.31C, Centre Scientifique et Technique du Bâtiment, 

Nantes, France.

3. Larose, G. and Smitt, L. (1999). “Rain/Wind Induced Vibrations of the Parallel Stay Cables 

for the Oresund High Bridge,” Proceedings of the IABSE Conference, Cable-Stayed Bridges, 

Malmö, Sweden.

4. Cheng, S., Larose, G., Savage, M., and Tanaka, H. (2003). “Aerodynamic Behaviour of an 

Inclined Circular Cylinder,” Journal of Wind and Structures, 6(3), 197–208.

5. Kumarasena, S., Jones, N., Irwin, P. and Taylor, P. (2007). Wind-Induced Vibration of Stay 

Cables, Report No. FHWA-HRT-05-083, Federal Highway Administration, McLean, VA.

6. Andersen, T., Jakobsen, J., Macdonald, J., Nikitas, N., Larose, G., Savage, M., and 

McAuliffe, B. (2009). “Drag-Crisis Response of an Elastic Cable-Model,” Proceedings of 

8th International Symposium on Cable Dynamics, 341–348, Paris, France.

7. Andersen, T. (2010). Wind Load on Inclined Circular Cylinder in Drag Crisis, Ph.D. Thesis,

University of Stavanger, Stavanger, Norway.

8. Flamand, O. and Boujard, O. (2009). “A Comparison Between Dry Cable Galloping and 

Rain-Wind Induced Vibrations,” Proceedings of 5th European African Conference On Wind 

Engineering, 485–488, Florence, Italy.

9. Cheng, S., Irwin, P., Jakobsen, J., Lankin, J., Larose, G., Savage, M., Tanaka, H., and Zurell, 

C. (2003). “Aerodynamic Behaviour of Cables Against Skew Wind,” Proceedings of 11th 

International Conference on Wind Engineering, 301–308, Lubbock, TX.

10. Nikitas, N., Macdonald, J., Andersen, T., Jakobsen, J., Savage, M., and McAuliffe, B. 

(2009). “Wind Tunnel Testing of an Inclined Aeroelastic Cable Model—Pressure and Motion 

Characteristics, Part I,” Proceedings of 5th European African Conference On Wind 

Engineering, Florence, Italy.

11. Jakobsen, J., Andersen, T., Macdonald, J., Nikitas, N., Savage, M., and McAuliffe, B. 

(2009). “Wind Tunnel Testing of an Inclined Aeroelastic Cable Model—Pressure and Motion 

Characteristics, Part II,” Proceedings of 5th European African Conference On Wind 

Engineering, Florence, Italy.

12. Larose, G., Savage, M., and Jakobsen, J. (2003). “Wind Tunnel Experiments on an Inclined 

and Yawed Circular Cylinder in the Critical Reynolds Number Range,” Proceedings of 11th 

International Conference on Wind Engineering, 1705–1712, Lubbock, TX.

205
13. Macdonald, J. and Larose, G. (2006). “A Unified Approach to Aerodynamic Damping and 

Drag/Lift Instabilities, and its Application to Dry Inclined Cable Galloping,” Journal of 

Fluids and Structures, 22(2), 229–252.

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HRDI-50/09-14(WEB)E