effect of geometric factors on lateral …docs.trb.org/prp/17-03950.pdf2 vehicles in freeway buffer...

EFFECT OF GEOMETRIC FACTORS ON LATERAL POSITION OF 1

VEHICLES IN FREEWAY BUFFER SEPARATED MANAGED LANES 2

3

By 4 5

Tomás E. Lindheimer, Ph.D. 6 (Corresponding Author) 7

Associate Transportation Researcher 8

Texas A&M Transportation Institute 3135 TAMU 9

College Station, TX 77843-3135 10

Phone: 979/458-2587, fax 979/845-6006 11

Email: [email protected] 12

13

Kay Fitzpatrick, Ph.D., P.E., P.M.P. 14 Senior Research Engineer 15

Texas A&M Transportation Institute, 3135 TAMU 16


Phone: 979/845-7321, fax: 979/845-6006 18


20

Raul Avelar, Ph. D., P.E., P.M.P. 21 Associate Research Engineer 22

Texas A&M Transportation Institute, 3135 TAMU 23


Phone: 979/845-7321, fax: 979/845-6006 25


27

Jeffrey D. Miles, P.E., P.T.O.E. 28 Texas Department of Transportation 29


31

32

33

Submission Date: August 1, 2016 34

Number of Words in Text: 4,958 35

Number of Tables / Figures: 9x250= 2,250 36

Total Equivalent Number of Words: 7,208 37

38

mailto:[email protected]




Lindheimer, Fitzpatrick, Avelar, Miles 1

ABSTRACT 39 Chapter 3 in the 2004 American Association of State Highway and Transportation Officials High 40

Occupancy Vehicle Guidelines includes a prioritized tradeoff table on various design options for 41

high occupancy vehicle lanes (now known as managed lanes). The design tradeoffs include the 42

reduction of lane, shoulder, and/or buffer width. The key measure believed to be affected by 43

lane, shoulder, and buffer width is lateral position. The objective of this study was to identify the 44

relationship between operations and cross-section width, including the type of buffer design 45

separating the managed lanes from the general-purpose lanes. This research study collected 46

lateral position data on existing managed lane facilities with a range of geometric elements 47

within both tangent and horizontal curves and identified potential relationships between the 48

geometric design element values and the measure of effectiveness. The field studies included 49

data collected at 28 sites using fixed video cameras and along 161 centerline miles using an 50

instrumented vehicle that recorded data for the vehicle immediately in front of the instrumented 51

vehicle. The study found that managed lane drivers shifted away from the pylons placed in the 52

buffer. Horizontal alignment (tangent or curve) and the direction of the horizontal curve (left or 53

right) were influential on lateral position. Left shoulder, lane, and buffer width affected lateral 54

position. Modifying a 6.5-ft shoulder to a minimum shoulder (i.e., 1.5 ft) will result in drivers 55

moving to the right about 0.5 ft; however, if a 18.5-ft shoulder is reduced by 5 ft, the impact in 56

operations is negligible (drivers would shift only about 0.11 ft toward the right). 57

58

59

60


INTRODUCTION 61 The 2004 American Association of State Highway and Transportation Officials (AASHTO) 62

High Occupancy Vehicle Guidelines (1) include tradeoff suggestions on various design options 63

for high-occupancy vehicle (HOV) facilities, now called managed lanes. Chapter 3 in the 64

Guidelines contains tables of the prioritized design tradeoffs which include the reduction of lane, 65

shoulder, and/or buffer width. Figure 1 shows the shoulder, lane, and buffer of the managed lane 66

in relation to general purpose traffic. The dimensions of a managed lane could possibly 67

influence driver behavior. Drivers may adjust their position in the managed lane depending on 68

their proximity to a concrete barrier or to traffic in the adjacent general-purpose lane. Those 69

adjustments may be different depending upon the available width for the shoulder, the lane, or 70

the buffer between the managed lane and the general-purpose lane. 71

72

73 FIGURE 1 Managed lane elements. 74

75

Objective 76 The objective of this study was to identify the relationship as revealed through travel data 77

between operations and cross-section width, including the type of buffer design separating the 78

managed lanes from the general-purpose lane. The researchers collected lateral position data on 79

existing managed lane facilities with a range of lane widths, shoulder widths, and buffer widths 80

within both tangent and horizontal curves and identified potential relationships between the 81

geometric design element values and the measures of effectiveness. 82

83

LITERATURE REVIEW 84 Previous studies on lateral position of vehicles within a driving lane mostly investigated two-lane 85

rural roads and curves. When looking at how the application of rumble strips affects the lateral 86

position of vehicles within the lane, researchers used piezoelectric sensors in a 87

Z-configuration (2). The same configuration using road tubes was deployed when investigating 88

lateral position and speed at horizontal curves (3,4). Fitzsimmons et al. analyzed the speed and 89


lateral position data for 23,468 vehicles traveling on two horizontal curves in central Iowa. The 90

tubes were placed in five equally spaced stations along the curve, and the spacing was 91

determined by the distance between the PC and PT points. The study used a linear mixed effects 92

model to attempt to predict speed and lateral position along curves. The researchers found that 93

vehicle type, time of day, and travel direction were significant factors affecting a vehicle’s speed 94

and lateral position. Researchers looked at driver behavior and found that speed entering the 95

curve has a direct impact on lateral position and acceleration near the center of the curve (3). 96

Hallmark et al. (4) performed an odds ratio analysis to correlate speed and lateral position 97

on curves. The study found that the odds of a near lane crossing were 2.37 to 4.47 greater at 98

higher speeds. These results were statistically significant and imply that the higher the speed the 99

greater the odds of a near lane crossing. Odds of a near lane crossing for vehicles traveling more 100

than 5 mph when compared to slower vehicles were not statistically significant. Gates et al. (5) 101

used video footage to gain insight on the impact of centerline and shoulder rumble strips on 102

driver behavior. High-definition cameras were mounted on poles (7 to 20 ft high) to record 103

traffic during daylight hours. Lateral position was measured according to the center of the lane 104

and the center of the vehicle with the license plate being the reference point. The vehicle was 105

considered centered if it was within 6 inches to the left or right of the center of the lane. The 106

study found that rumble strips had a significant impact on lateral position on curve and tangent 107

segments. Variations existed between vehicle types, but overall vehicles tended to travel down 108

the center of the lane when both center and shoulder rumble strips were present. 109

Bunker et al. (6) used video footage to look at lateral position of cars and heavy vehicles 110

on two-lane highways in Queensland, Australia. What was of interest was the interaction of 111

passenger cars with freight vehicles towing two or more trailers. Lateral position was used as a 112

measure to assess driver behavior. For data collection a camera was on an overpass overlooking 113

the road. Lateral position was defined as the distance between the middle of the road and the 114

nearest edge of the vehicle. Lateral position was measured off the video image by using a scaled 115

overlay on the computer screen. The scale divided each lane into eight divisions. Four hours of 116

video was recorded and a total of 3,151 vehicles were observed. The study showed that typically 117

passenger cars do not change their lateral position when heavy trucks travel in the opposite 118

direction. They also found that heavy trucks tend to occupy part of the shoulder, while passenger 119

cars tend to straddle the edgeline marking that separates the shoulder and the lane. 120

Researchers in Sweden investigated the lateral position and lateral wander (i.e. variation 121

of lateral position) of vehicles and the effect they have on pavement surface wear. Lateral 122

position was measured from the edge of the right front tire to the edge of the right hand side. 123

Researchers collected data from 21 different sites by using three coaxial cables placed in a “Z” 124

configuration within the right hand side lane of the roadway. The investigation was carried out in 125

tangent segments of the roadway and not on curved segments. Lateral position data of over 126

271,000 vehicles was gathered and analyzed. The analysis showed that lateral wander is affected 127

by lane width, verge width, total width of the roadway, and proximity to guardrail. Lateral 128

wonder for smaller vehicles had a higher variation (7.5 to 17.9 inches) than commercial vehicles 129

(5.5 to 16.9 inches). The researchers hypothesize that curvature will have an effect on lateral 130

position (7). 131

In summary, the literature review identified two methods of gathering data for lateral 132

position: use of on-pavement sensors or road tubes, and use of video cameras overlooking a 133

roadway segment. Lateral position research has been a concern mainly on curves and tangent 134


segments of two-lane rural highways. Researchers have used lateral placement as a measure to 135

determine driver behavior and have not researched to identify a relationship with crash rates. 136

137

DATA COLLECTION 138 Data were collected during daylight and dry pavement conditions. Video data using a fixed video 139

camera were obtained from San Jose, CA; Houston, TX; within the Minneapolis/St. Paul, MN 140

region; and within the Puget Sound, WA region. These data were retrieved from either 141

contacting the operating agencies directly or having a research team place stationary cameras in 142

the field. Data from the San Jose, Minnesota, and Washington sites were obtained by contacting 143

the Santa Clara Valley Transportation Authority, the Minnesota Department of Transportation, 144

and the Washington State Department of Transportation, respectively. Individuals from all 145

agencies provided the research team with video samples representing either a period or an entire 146

day of operation. The focal point for each camera was centered on the managed lane, with the 147

background capturing traffic conditions from the adjacent general-purpose lanes. Cameras 148

captured either a period of observed traffic (e.g. morning, afternoon), or an entire day or two of 149

operation depending upon what the agency could provide. Data from the Houston, TX, location 150

were obtained from stationary cameras installed on the concrete barrier separating the direction 151

of travel. Cameras in-site recorded traffic for a 24-hour period. 152

An instrumented vehicle was used to obtain in-field data for a selection of sites. For this 153

protocol, an instrumented vehicle followed a vehicle traveling in the managed lane. The 154

instrumented vehicle was outfitted with a still-frame video camera, a LIDAR detector, and a GPS 155

data logger. The still-frame video camera captured single black-and-white images, recording the 156

images once per second. The LIDAR detector measured the distance from the instrumented 157

vehicle to the followed vehicle. The GPS data logger recorded the geographical coordinates 158

(latitude, longitude) and speed of the instrumented vehicle. Data from each instrument were 159

transmitted into an onboard laptop computer. 160

161

SITE SELECTION 162 Sites were chosen based on geographic distribution and variety in design widths. The research 163

team considered sites in California, Minnesota, Texas, and Washington. Only sites with one 164

managed lane per direction and buffer-separated from the general purpose lanes were considered. 165

The geometric characteristics obtained for each site included physical components of the 166

managed lane, adjacent general-purpose lane, and other traits within the corridor. Data on 167

geometric features were gathered through discussion with local agencies responsible for 168

operating the managed lane, measurements from aerial photographs, or measurements taken 169

when installing the fixed video cameras. Specifically, the following geometric features were 170

collected for use in the study: 171

Left shoulder width. 172

Managed lane width. 173

Lane separation type between managed lane and general-purpose lanes (e.g. flush 174

buffer, pylons). 175

Buffer width. 176

Buffer type (described below). 177

Number of general-purpose lanes. 178

Average lane width for the general-purpose lanes. 179

Right shoulder width. 180


The following buffer types were observed during the study: 181

Double white lines (DW), see Figure 2 (a). 182

Single white and four yellow lines (SWFY), see Figure 2 (b). 183

Double white lines with pylons (DWP) see Figure 2 (c). 184

Single white line and single yellow line (SWSY). 185

Single white line and two yellow lines (SWTY) see Figure 2 (d). 186

Single white line (SW). 187

Pylons, where present, were 36 to 39 inched high and were spaced 12 to 14 ft apart. 188

189

(a) (b)

(c) (d)

FIGURE 2 Examples of buffer types observed during the study. 190 191

Data were collected through fixed camera video footage or by an instrumented vehicle 192

outfitted with appropriate sensors and video recorders. For driving data, freeways in and near the 193

city of Dallas were chosen because of the use of pylons serving as a barrier between the managed 194

lane and the general-purpose lanes. In California, freeways were chosen to provide a range of 195

buffer widths. The routes and data collection times for the driving data were selected to increase 196

the number of potential data points while being on segments of interest. The research team 197

gathered driving data from a total of 11 routes; 9 in California and 2 in Texas. The following 198

buffer types (and widths shown in parentheses), lane widths, and shoulder widths were observed 199

during the study: 200

Lane width: managed lane (10.4 – 11.8 ft), general-purpose lane (11 – 12 ft). 201

Shoulder width (1.4 – 14.9 ft). 202

Buffer type: DW (1 – 4.5 ft). 203

Buffer type: SWTY (1.7 – 4.9 ft). 204

Buffer type: SWFY (4.1 – 4.9 ft). 205

Buffer type: SWSY (1.7 – 2.2 ft). 206

Buffer type: DWP (4 – 5 ft). 207

There were a total of 28 sites where data were gathered with fixed video cameras. Seven 208

sites were located in Minnesota, 10 in Texas, 10 in Washington, and one in California. Managed 209

lane facilities in Minnesota, California and Texas had limited access, while Washington facilities 210


have continuous access. The following buffer types (and widths shown in parentheses), lane 211

widths, and shoulder widths were observed during the study: 212

Lane width: managed lane (10 – 13 ft), general-purpose lane (11 – 12 ft). 213

Shoulder width (1.67 – 18.35 ft). 214

Buffer type: DW (1 – 4.67 ft). 215

Buffer type: DWP (5 ft). 216

Buffer type: SW (1 ft). 217

218

DRIVING AND FIXED VIDEO DATA REDUCTION 219 For this research, lateral position was defined as the space between the edge of the back wheel 220

and the inside edge of the pavement marking. Figure 3 illustrates the left lateral position (LP-Lf) 221

and the right lateral position (LP-Rt) for a vehicle in a managed lane. 222

223

224 Source: TTI 225

FIGURE 3 Example of left and right lateral position for vehicle near center of the managed 226

lane 227

228 The following data variables were collected for each vehicle: 229

Time of day. 230

Type of vehicle. 231

Presence of an adjacent vehicle in the general-purpose lane. 232

General-purpose lane traffic was traveling 10 mph slower than the managed lane, in 233

the opinion of the technician. 234

Lateral position of the vehicle within the managed lane. 235

Lateral position data were reduced from the video on desktop computers. To determine 236

lateral position, a transparency sheet was placed over the computer monitor. The pavement 237

marking lines and a perpendicular line across the lane were drawn on the transparency. Road 238

features (such as diamond markings) or vehicle features (i.e. rear bumper) were used to draw a 239


horizontal line across the lane in order to ensure that the horizontal line was perpendicular to the 240

pavement markings, and straight according the plane of the video. A ruler was aligned to the 241

horizontal line and the tick mark “0” was placed along the inside edge of the pavement marking 242

and then the tick marks from the left pavement marking to the wheel were noted. After the lateral 243

position in millimeters was read, the lane width was measured with the ruler. For some videos it 244

was better to measure the right wheel instead of the left wheel. Lane width measurements were 245

taken in the field or using aerial photographs for each site where video footage was recorded. 246

These measurements allowed the research team to scale the lateral position readings from 247

millimeters to feet for each vehicle observed. 248

For the data from the instrumented vehicle each photograph was automatically saved with 249

a time stamp depicting the date and time of day the picture was captured. All LIDAR readings 250

and GPS coordinates were entered into a spreadsheet and matched according to the time stamp of 251

when the data point was recorded. A researcher would enter on the spreadsheet the following 252

information from the picture: 253

Is the vehicle within an access opening or entrance/exit point? Vehicle within an 254

access opening or at entrance/exit points were not reduced. 255

Is the vehicle on a tangent (T), a curve to the left (LC), a curve to the right (RC). 256

Pixel coordinates for the left pavement marking. 257

Pixel coordinates for the edge of the right rear wheel of the car. 258

Pixel coordinates for the right pavement marking. 259

Only pictures with a clear resolution and with all road features visible were used in data 260

reduction. The picture file was opened with Microsoft Paint to obtain the pixel coordinates of the 261

right wheel and the inside edge of the pavement marking. Once all pixel coordinates were 262

entered, the difference between pixel coordinates was calculated. The LIDAR distance was used 263

to determine the reference scale from millimeters on the screen to estimated feet within the 264

managed lane. To ensure data quality, limits for non-realistic outliers were set for lane width. 265

Data were also not used for occurrence when lane readings were below 9 ft or above 13 ft. Both 266

occurrences could be due to an error in LIDAR reading, or due to difficulties in aiming the 267

LIDAR gun. All valid data points where compiled into a main database for analysis. This 268

calibration, and other tests of the procedure, further ensured that lateral position readings were 269

accurate within 6 inches. 270

When reducing the dataset, some data points represented the left lateral position and 271

some represented the right lateral position depending upon which side of the vehicle provided the 272

better view. Because most of the dataset was left lateral position, the right lateral positions were 273

converted to be left lateral position through the use of the following assumed vehicle wheel base 274

widths: 275

Passenger car = 6.0 ft, based on Green Book Figure 2-1 (8). 276

SUV / Van = 6.0 ft, based on Green Book Figure 2-2 (8). 277

Pickup Truck = 6.5 ft, estimated from: http://dodgeram.info/2001/dimensions.html and 278

https://www.fleet.ford.com/truckbbas/topics/2012/12_SD_Pickups_SB.pdf. 279

Transit or school bus = 8.5 ft, based on Green Book Figure 2-4 (8). 280

Emergency vehicle = 8.0 ft, based on following website: 281

http://www.hortonambulance.com/type1.cfm. 282

Motorcycle = 2.3 ft, estimated from: 283

https://www.fleet.ford.com/truckbbas/topics/2012/12_SD_Pickups_SB.pdf. 284

The resulting dataset included over 7000 vehicles. 285

http://www.hortonambulance.com/type1.cfm

https://www.fleet.ford.com/truckbbas/topics/2012/12_SD_Pickups_SB.pdf


DRIVING AND FIXED VIDEO FINDINGS 286 287

Preliminary Findings 288 The average and standard deviation for lateral position (left) is shown in Table 1 for the driving 289

sites and in Table 2 for the fixed video camera sites. These tables also provide the total number 290

of lateral position readings available for the analysis. Overall, the vehicles in the managed lane 291

were about 2.5 ft from the left edgeline. 292

293

TABLE 1 Average left lateral position by site for driving sites. 294 Site

a SW (ft) LW (ft) BW (ft) Buffer Count Ave Lf_LP StdDev Lf_LP

CA I-10 12.8 11.3 4.9 DW, SWTY 180 2.9 0.9

CA I-105 9.4 11.0 4.9 SWFY 205 2.9 0.8

CA I-210 2.7 11.1 1.9 SWTY 348 2.8 0.8

CA I-405 2.7 10.4 1.7 SWTY 144 2.9 0.8

CA I-605 2.2 10.4 2.2 SWSY 26 2.6 0.8

CA SR-118 2.2 11.7 2.4 SWTY 172 3.3 1.1

CA SR-134 1.8 10.9 1.7 SWSY 142 3.0 0.8

CA SR-210 14.9 11.8 4.1 SWFY 83 2.6 0.8

CA SR-60 1.4 10.5 1.7 SWTY 8 2.9 0.6

CA SR-91 1.8 10.9 2.0 SWTY 13 3.3 1.2

TX I-635 2.0 10.5 5.0 DWP 865 2.4 0.8

TX US-75 2.0 11.0 4.0 DWP 1169 2.0 0.8

All Sites NA b NA NA NA 3355 2.5 0.9

a Column Headings

Site = Name of site consisting of state and highway number.

SW = left shoulder width (ft).

LW = managed lane width (ft).

BW = buffer width (ft).

Buffer = buffer type.

Count = number of vehicles included in dataset.

Ave Lf_LP = average left lateral position.

StdDev Lf_LP = standard deviation for left lateral position. b NA = value not applicable or meaningful for all site totals or averages.

295

296


TABLE 2 Average left lateral position by site for fixed view sites. 297 Site

a Road LA

or

CA

Tan

or

Cur

SW

(ft)

LW

(ft)

BW

(ft)

Buffer Count Ave

Lf_LP

StdDev

Lf_LP

CA 01 SR-237 LA Tan 4.0 11.0 2.0 DW 1097 1.9 1.0

MN 6091 I-35W LA Tan 4.0 10.0 3.0 DW 203 1.2 0.9

MN 6131 I-35W LA Tan 3.0 10.5 2.0 DW 191 1.7 0.9

MN 614 I-35W LA Tan 3.0 10.0 3.0 DW 109 1.7 1.2

MN 6231 I-35W LA Tan 2.0 12.0 0.8 SY 203 3.9 1.3

MN 908 I-394 LA Tan 8.0 11.8 2.0 DW 152 3.0 1.0

MN 909 I-394 LA Tan 8.5 11.5 3.0 DW 132 2.4 1.2

TX 01 US-59 LA Tan 9.8 11.5 1.0 DW 190 1.8 1.5

TX 02 US-59 LA Tan 9.9 11.2 1.0 DW 184 2.2 1.3

TX 03 I-10 LA Tan 18.4 13.0 5.0 DWP 114 3.9 1.5

TX 04 I-10 LA Tan 15.3 13.0 5.0 DWP 100 2.2 0.9

TX 05 US-59 LA Tan 13.3 11.3 4.7 DW 187 3.1 1.2

TX 06 US-59 LA Tan 13.4 11.5 4.5 DW 289 3.0 1.3

TX 07 US-290 LA Tan 1.7 10.5 0.8 DW 179 2.7 0.8

TX 08 US-290 LA Tan 1.7 10.5 0.8 DW 119 2.9 0.8

TX 09 US-290 LA Tan 1.7 10.5 0.8 DW 142 2.8 0.8

TX 10 US-290 LA Tan 1.7 10.5 0.8 DW 107 2.7 0.8

WA-01 SR-167 CA Tan 9.50 11.0 1.00 SW 177 2.3 1.0

WA-02 SR-167 CA Tan 7.77 11.3 1.00 SW 170 2.5 0.9

WA-03 SR-167 CA Tan 8.50 10.2 2.00 DW 108 1.9 0.8

WA-04 SR-167 CA Tan 6.47 12.8 1.00 SW 104 2.7 1.0

WA-05 SR-167 CA Tan 8.35 12.2 1.00 SW 108 3.5 1.0

WA-06 SR-167 CA Tan 11.00 12.2 1.00 SW 111 3.4 1.2

WA-07 SR-167 CA Cur 8.35 12.2 1.00 SW 108 0.8 0.8

WA-08 SR-167 CA Cur 11.00 12.2 1.00 SW 198 1.8 0.8

WA-09 SR-167 CA Cur 9.50 11.0 1.00 SW 107 3.1 1.0

WA-10 SR-167 CA Cur 7.77 11.3 1.00 SW 116 3.1 1.1

All Sites NA b NA NA NA NA NA NA 5005 2.5 1.0

a Column Headings

Site = Name of site.

Road = name of road for site.

LA or CA = Limited access (LA) or continuous access (CA).

Tan or Cur= Tangent (T) segment or curve (C) segment of highway.

SW = left shoulder width (ft).

LW = managed lane width (ft).

BW = buffer width (ft).

Buffer = buffer type.

Count = number of vehicles included in dataset.

Ave Lf_LP = average left lateral position.

StdDev Lf_LP = standard deviation for left lateral position. b NA = value not applicable or meaningful for all site totals or averages.

298 299


STATISTICAL EVALUATIONS 300 301

Variable Selection 302 During preliminary evaluations, characteristics of the dataset that needed to be considered during 303

the evaluation were identified. As expected, narrow lane widths were typically associated with 304

narrow shoulder and buffer widths. If that relationship is always true, then the shoulder, lane, and 305

buffer widths would be correlated, and not all variables would be able to be in the model. By 306

combining the driving and fixed video camera datasets, sufficient variability in shoulder, lane, 307

and buffer widths exists so that all three variables can be uniquely included. 308

In addition to the site characteristics and level of access, conditions present when the 309

lateral position reading was taken could affect a driver’s decision. The type of vehicle, especially 310

motorcycles, has an obvious influence on lateral position. Other conditions measured included 311

whether a vehicle in the neighboring general-purpose lane was near the managed lane vehicle 312

and whether the technician believed the managed lane vehicle’s speed could be 10 mph higher 313

than the general-purpose lanes. While a neighboring general-purpose vehicle could be next to the 314

managed lane vehicle without having the 10-mph speed difference, for this dataset these 315

variables were highly correlated. Therefore, only one of the two variables (vehicle in 316

neighboring lane or managed lane vehicle more than 10 mph higher) could be retained in the 317

model. The team selected the variable for whether a neighboring general-purpose vehicle was 318

present because stronger statistical models resulted. 319

320

Statistical Model 321 A linear mixed-effect model was used to analyze the lateral position data. Initial models did not 322

produce very satisfactory results, so the sites and data were reviewed to identify other variables 323

or other relationships that could help to explain the variations observed. Two changes were 324

identified. The variable pylon (yes or no) was added as it appears that left lateral position is 325

smaller for those sites with pylons. The other change was to model the shoulder, lane, and buffer 326

widths as parabolic curves. An advantage to using the parabolic curve function is that it reflects 327

changes in width having minimal influence when the width is large and having much greater 328

influence when the width is small. A parabolic curve has a portion where the curve is decreasing 329

to a vertex after which it will then be increasing. To improve the ability to easily interpret the 330

results, the vertex of the curves were set to fall outside the available range for the variable. 331

The best fit model is shown in Table 3. This table also shows variable definitions and 332

baseline conditions of the model. The sign of lane width and shoulder width should be 333

interpreted in the opposite direction than the rest of variables because of how these shifted 334

variables were defined. The results demonstrate that in most cases the lateral position for most of 335

the vehicle types is significantly different from a passenger car. As anticipated, larger vehicles 336

(e.g., buses) were closer to the left edgeline while motorcycles are farther from the edgeline. 337

When a general-purpose vehicle is next to the managed lane vehicle, the managed lane vehicle 338

was 0.32 ft closer to the edgeline. 339

340


TABLE 3 Linear mixed-effect model. 341 Variable

a, b Estimate Std. Error DF t-value p-value

Reference c 3.14528 0.22674 8310 13.87173 >0.00001

TpVeh=B -1.23188 0.07862 8310 -15.66793 >0.00001 d

TpVeh=EM -0.39833 0.245064 8310 -1.62546 0.1041 d

TpVeh=MC 1.92241 0.08664 8310 22.18856 >0.00001 d

TpVeh=PT -0.27951 0.03267 8310 -8.55412 >0.00001 d

TpVeh=V 0.092721 0.02188 8310 4.23762 >0.00001 d

Veh_GP=Yes -0.31771 0.02037 8310 -15.59416 >0.00001

Pylons=yes -0.92541 0.37144 34 -2.49143 0.0178

sqBW 0.03180 0.01421 34 2.23837 0.0319

sqLW.r14 -0.13387 0.02738 34 -4.88866 >0.00001

sqSW.r19 0.00361 0.00114 34 3.16544 0.00033

HorAl=LC -1.69920 0.20453 8310 -8.30779 >0.00001

HorAl=RC 0.44487 0.09033 8310 4.92481 >0.00001

sqBW:HorAl=LC 0.03796 0.00548 8310 6.91957 >0.00001

sqBW:HorAl=RC -0.01289 0.00584 8310 -2.20807 0.0273

sqSW.r19:HorAl=LC 0.00357 0.00065 8310 5.50724 >0.00001

Notes:

a Column Headings:

Estimate = natural logarithm of the ratio: Odds (coefficient level) / Odds (reference level). In the case of

reference level, Estimate is the log-odds of the average yielding rate at the reference level.

Std. Error = Standard error of value.

DF = degree of freedom

t-value = conservative estimate of the z-value, which is the standard normal score for estimate, given the

hypothesis that the actual odds ratio equals one.

p-value = Probability that the observed log-odds ratio be at least as extreme as estimate, given the

hypothesis that the actual odds ratio equals one. b Variables included in the statistical evaluation:

TpVeh = Type of vehicle: Passenger Car (PC), Pickup Truck (PT), SUV/Van (V), Transit or

School Bus (B), Emergency Vehicle (EM), Motorcycle (MC)

Veh_GP = was there a general-purpose vehicle next to managed lane vehicle? (yes or no)

Pylons = were pylons present? (yes or no)

sqBW = square of buffer width

sqLW.r14 = square of lane width with a reference point of 14

sqSW.r19 = square of shoulder width with a reference point of 19

HorAl = horizontal alignment, left curve (LC), right curve (RC), or tangent (Tan) c Baseline condition left lateral position in the model is estimated for the following conditions:

TpVeh = PC

Veh_GP = No

Pylons = No

HorAl = Tan d These p-values require an adjustment for multiple comparisons if inferences about different lateral

position values among vehicles are intended.

342

The results of the statistical evaluation can be used to develop a lateral position prediction 343

equation as shown in equation 1. 344

345

LP_Lf = 3.14528 + 0 (TpVeh=PC) – 1.23188(TpVeh=B) – 0.39833 (TpVeh=EM)


+ 1.92241 (TpVeh=MC) – 0.27951 (TpVeh=PT) + 0.09272 (TpVeh=V)

– 0.31771 (Veh_GP=Yes) –0.92541 (Pylons=yes) + 0.03180 (BW)^2

– 0.13387 (14-LW)^2 + 0.00361 (19-SW)^2 + 0 (Hor=Tan) –1.69920 (Hor=LC)

+ 0.44487 (Hor=RC) + 0.03796 (BW)^2 × (Hor=LC) – 0.01289 (BW)^2 × (Hor=LC)

+ 0.00357 (19-SW)^2 × (Hor=LC)

Equation 1 346 Where: 347

LP_Lf = Left lateral position within the managed lane, in other words the 348

distance between the left wheel of the vehicle and the edgeline between the 349

managed lane and the shoulder (ft). 350

TpVeh=PC = 1 when the vehicle type is a passenger car, 0 otherwise. 351

TpVeh=B = 1 when the vehicle type is a bus, 0 otherwise. 352

TpVeh=EM = 1 when the vehicle type is an emergency vehicle, 0 otherwise. 353

TpVeh=MC = 1 when the vehicle type is a motorcycle, 0 otherwise. 354

TpVeh=PT = 1 when the vehicle type is a pickup truck, 0 otherwise. 355

TpVeh=V = 1 when the vehicle type is a van, 0 otherwise. 356

Veh_GP=Yes = 1 when a vehicle is present in the general-purpose lane next to the 357

managed lane vehicle, 0 otherwise. 358

Pylons=yes = 1 when pylons are present in the buffer, 0 otherwise. 359

BW = Buffer width (ft). 360

LW = Lane width (ft). 361

SW = Shoulder width (ft). 362

Hor=Tan = 1 when the horizontal alignment is a tangent, 0 otherwise. 363

Hor=LC = 1 when the horizontal alignment is a curve to the left, 0 otherwise. 364

Hor=RC = 1 when the horizontal alignment is a curve to the right, 0 otherwise. 365

366

According to the model in equation 1 drivers shy away from the pylons. When pylons 367

were present, drivers were 0.93 ft closer to the left edgeline as compared to when the pylons 368

were not present. Horizontal alignment and the direction of the horizontal curve were influential 369

on lateral position. Drivers were closer to the left edgeline by up to 1.7 ft when on a curve to the 370

left and drivers shifted farther from the left edgeline by up to 0.44 ft when on a curve to the right 371

depending upon assumed shoulder, lane, and buffer widths. The model also tested if access to the 372

managed lane (i.e. continuous vs. limited access) had an effect on lateral position. The variable 373

was found not significant; therefore, it was not included in the final model. 374

375

Illustration of Lateral Positions for Key Variables 376 Figure 4 illustrates the relationship between lateral position and shoulder width. Note that the 377

graph is a plot of regression findings showing results for the complete range between the 378

minimum of 1.5 ft and the maximum of 18.5 ft. For some agencies, shoulders more than 4 ft and 379

less than 8 ft are avoided because drivers may believe sufficient width is available for refuge. 380

The plot shows that when the left shoulder of a tangent section or a horizontal curve to the right 381

is at the minimum for the dataset (about 1.5 ft), drivers tend to be 1.11 ft farther to the right of 382

the left edgeline (i.e., left lateral position increases), compared to when shoulder width is 18.5 ft. 383

This curved function also implies that modifying a 6.5 ft shoulder to a minimum shoulder (i.e., 384

1.5 ft) will result in drivers moving to the right about 0.54 ft; however, if a 18.5 ft shoulder is 385


reduced by 5 ft, the impact in operations is negligible (drivers would shift only about 0.11 ft 386

toward the right). The effects were more pronounced for drivers on curves to the left, which limit 387

sight distance more than tangents or curves to the right. Drivers on a section with minimal 388

shoulders appear to be more concerned with avoiding the median barrier when turning left as 389

demonstrated by the larger left lateral position distances. 390

391

392 FIGURE 4 Lateral position relative to changes in shoulder width. 393

394

Smaller lane widths logically result in smaller left lateral positions because the 395

measurement is a reflection of the lane width. As lane width decreases, drivers are closer to the 396

left edgeline as shown in Figure 5. The plot shows that when the lane width is at the minimum 397

for the dataset (10.5 ft), drivers tend to be 1.6 ft closer to the left edgeline (i.e., left lateral 398

position decreases), compared to when lane width is 13.5 ft. A curvilinear relationship implies 399

different effects at different levels of lane width. When reducing a 13-ft lane by 1 ft, the model 400

predicts a shift toward the left of about 0.41 ft. However, when reducing an 11.5-ft lane by 1 ft, 401

the result would be drivers shifting toward the left by about 0.8 ft. 402

403


404 FIGURE 5 Lateral position related to lane width. 405

406

The width of the buffer affects lateral position with larger widths having more influence 407

than smaller widths, as shown in Figure 6. The interaction between buffer width and horizontal 408

alignment also affects lateral position. The presence of a horizontal curve to the left was more 409

influential than a tangent section or a horizontal curve to the right. A difference of about 0.9 ft in 410

lateral position exists between 5 ft and 0.8 ft buffers on tangents, whereas left curves there was a 411

difference of 1.9 ft. The curvilinear relationship for tangents indicates that reducing a 2-ft buffer 412

to a 1-ft buffer will have a negligible effect (a shift to the left of approximately 0.1 ft) compared 413

to reducing a 5-ft buffer to 4 ft (a shift to the left about 0.3 ft). When on a left turning curve, 414

drivers are 0.84 ft closer to the left shoulder with a 2-ft buffer as compared to a 4-ft buffer. 415

416

417 FIGURE 6 Lateral position relative to buffer width. 418

419

420


SUMMARY / CONCLUSION 421 This study identified potential tradeoffs in cross section dimensions by gathering the lateral 422

position of vehicles within existing managed lanes with different shoulder, lane, and buffer 423

widths. The field studies included data collected at 28 sites using fixed video cameras and along 424

161 centerline miles using an instrumented vehicle that recorded data for the vehicle 425

immediately in front of the instrumented vehicle. The key measure was lateral position of the 426

managed lane vehicle measured between the shoulder edgeline and the left rear wheel. A 427

summary of the findings for variables that affect lateral position follow: 428

Vehicle type affects lateral position. Larger vehicles, such as buses, are closer to the 429

shoulder edgeline while smaller vehicles, such as motorcycles, are a greater distance 430

away. 431

Presence of a vehicle in the neighboring general-purpose lane results in the managed 432

lane vehicle shifting closer to the shoulder edgeline. 433

Pylons in the buffer result in managed lane drivers shifting away from the pylons. 434

Horizontal alignment (tangent or curve) and the direction of the horizontal curve (left 435

or right) are influential on lateral position. 436

Left shoulder, lane, and buffer width affect lateral position. The best statistical model 437

used a parabolic curve to model the relationships resulting in smaller values for those 438

elements having greater influence on the lateral position. For example, modifying a 439

6.5-ft shoulder to a minimum shoulder (i.e., 1.5 ft) will result in drivers moving to the 440

right about 0.5 ft; however, if a 18.5-ft shoulder is reduced by 5 ft, the impact in 441

operations is negligible (drivers would shift only about 0.11 ft toward the right). 442

443

The speed of the lead vehicle for the data collected using the instrumented vehicle was 444

also considered; however, it was found to be not significant for this dataset. The variable 445

concerning types of access to the managed lane was considered but found to be not significant. 446

Another variable considered but found to be not significant was an estimate of whether the 447

managed lane vehicle was more than 10 mph faster than the neighboring general-purpose lane 448

vehicles. 449

Based on the findings, the following changes to practice can be considered: 450

The provision of adequate shoulder width is desirable because drivers are shying away 451

from the concrete median barrier. Research findings indicated that lateral position is 452

highly affected for narrow shoulder widths; however, a buffer can offset this impact. 453

Research findings show that the impact on lateral position is greater within the 454

minimal values for shoulder, lane, and buffer widths. For example, a 1-ft reduction in 455

shoulder width results in greater changes in lateral position when the shoulder width is 456

near minimal values (e.g., 2 or 4 ft) as compared to when the shoulder width is near 457

desirable (e.g., 8 ft or 14 ft). 458

If insufficient space is available for a full-width left shoulder, consider splitting the 459

available width between the left shoulder and a buffer. Managed lane vehicles are 460

closer to the center of the lane when these values are similar. 461

The practice of reducing the lane width by 1 ft (from 12 ft to 11 ft) and providing that 462

ft of width to the buffer is appropriate. 463

The use of pylons affects lateral position. Using the pylons within a wider buffer can 464

offset the impacts on lateral position. 465


As expected, driver’s lateral position is affected by horizontal curvature. Consider 466

providing additional buffer or shoulder widths within horizontal curves as drivers are 467

shifting their lateral positions when driving on a horizontal curve, especially horizontal 468

curves to the left. 469

470

ACKNOWLEDGMENTS 471 The material in this paper is from the National Cooperative Highway Research Program 472

(NCHRP) project 15-49, “Guidelines for Implementing Managed Lanes.” The research is 473

sponsored by the American Association of State Highway and Transportation Officials 474

(AASHTO), in cooperation with the Federal Highway Administration (FHWA), and is 475

conducted in the National Cooperative Highway Research Program, which is administered by the 476

Transportation Research Board of the National Research Council. The opinions and conclusions 477

expressed or implied in this paper are those of the authors. They are not necessarily those of the 478

Transportation Research Board, the National Research Council, the Federal Highway 479

Administration, the American Association of State Highway and Transportation Officials, or the 480

individual states participating in the National Cooperative Highway Research Program. The 481

authors appreciate the efforts of the numerous TTI staff and student workers who collected and 482

reduced the NCHRP 15-49 data used in this research or who assisted with other facets of the 483

research, especially Nick Wood and Dan Walker. 484

485


REFERENCES 486 1 AASHTO. Guide for High-Occupancy Vehicle (HOV) Facilities. American Association 487

of State Highway and Transportation Officials, Washington, DC, 2004. 488

2 Finley, M. D. Impact of Shoulder and Centerline Rumble Strips on Vehicle Lateral 489

Position on Two-Lane Roadways. ITE 2010 Annual Meeting and Exhibit. 2010. 490

3 Fitzsimmons, E. J., V. Kvam, R. R. Souleyrette, S. S. Nambisan, and D. G. Bonett. 491

Determining vehicle operating speed and lateral position along horizontal curves using 492

linear mixed-effects models. Traffic Injury Prevention 14, No. 3, pp. 309-321, 2013. 493

4 Hallmark, S. L., N. Hawkins, and O. Smadi. Relationship between Speed and Lateral 494

Position on Curves. 16th International Conference Road Safety on Four Continents. 495

Beijing, China (RS4C 2013), pp. 15-17, Statens väg-och transportforskningsinstitut, 496

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5 Gates, T.J, P.T. Savolainen, T.K. Datta, R.G. Todd, B. Russo, and J.G. Morena. Use of 498

both centerline and shoulder rumble strips on high-speed two-lane rural roadways: impact 499

on lateral position and passing maneuvers of vehicles. In Transportation Research 500

Record: Journal of the Transportation Research Board No. 2301, 2012, pp. 36-45. 501

6 Bunker, J. M., and A. Parajuli. Examining lateral positions of cars and heavy vehicles on 502

a two lane, two way motorway. Transport Engineering in Australia 10.2, pp. 129-139, 503

2006. 504

7 McGarvey, T. Vehicle Lateral Position Depending On Road Type And Lane Width: 505

Vehicle Position Surveys Carried Out On The Swedish Road Network. VTI rapport 506

892A. Statens väg-och transportforskningsinstitut, 2016. 507

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