Analysis of Naturalistic Driving Study Data: Roadway Departures on Rural Two-Lane Curves (2014)

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37 C h a p t e r 7 This chapter discusses the second research question: What defines normal curve negotiation? A methodology proposed by several other researchers was used to develop a relationship between tangent speed and off­ set and curve speed and offset, which was used to define nor­ mal curve driving. This relationship assumes that there is some relationship between the tangent and curve speed (drivers who speed upstream are also likely to speed within the curve) and between lateral offset upstream and within the curve (drivers who do not maintain lane position upstream will have similar lane keeping within the curve). Schurr et al. (2002) developed a relationship between the operating speed on tangent sections 183 m upstream and at the curve midpoint. Stodart and Donnell (2008) collected data upstream and within six curves using instrumented vehicles with 16 research participants. They compared change in speed and lateral position from the upstream tangent to the curve midpoint using the following: ∆ = − ∆ = − MPT MC MPT MC V V V L L L where V = speed; L = lateral position; MPT = midpoint of tangent; and MC = midpoint of curve. The objective of Research Question 2 was to define normal curve driving. Understanding how a driver normally negoti­ ates a curve during various situations provides insight into not only how characteristics of the roadway, driver, and envi­ ronment potentially influence how a driver drives, but also the areas that can lead to roadway departures. Knowing how much drivers normally deviate in their lane, as well as how they choose their speed, could potentially have implications on policy or design. Data Sampling and Segmentation approach for research Question 2 The conceptual model of curve driving assesses changes in metrics as the driver negotiates the curve based on the factors of the curve and driving behavior upstream of the curve. Data for several positions along the curve were sampled from the time series data from the DAS, which also had additional variables such as driver characteristics and environmental characteristics. The sampling plan for the curve model can be seen in Fig­ ure 7.1. Data were sampled at each point shown (e.g., PC); the locations for sampling were determined after plotting events and determining which sampling scheme picked up the com­ mon patterns identified. Sampling in the tangent section was based on distance. Sampling within the curve was at equi­ distant points rather than at a specified distance because the curves have varying lengths. The points sampled within the curve were the PC, PT, and then four equally spaced points (C1, C2, C3, and C4, as shown in Figure 7.1). Upstream data were collected every 50 m up to 300 m. These locations were chosen to capture driving upstream of where drivers react to the curve (i.e., normal tan­ gent driving) along with the area where they react and as they approach the entry to the curve. Because the data sampling plan required 300 m of upstream data, the analysis included only isolated curves (i.e., no S­curves or compound curves) and curves with a tangent section that was at least 300 m from the nearest upstream curve. DAS variables were sampled at each point shown. The vari­ ables included offset; speed; environmental characteristics, such as whether there was an oncoming vehicle or whether the driver was following another vehicle; and driver kine­ matic data, such as glance and distraction. Data collected for the upstream area included the offset and speed at each sam­ ple point, along with driver glance location and distractions. Analysis for Research Question 2

38 In addition, as noted previously, a moving average method was used to smooth data across rows (0.5­s intervals) to reduce noise present in the variables. These data were merged with environmental and driver data. The complete list of variables collected is included in Chapter 4. Because vehicle offset was the crash surrogate used for this research question, the offset data had to be quite accurate, as small changes in the offset could drastically affect the results of the model. Additionally, only isolated curves with a distance of 400 m or more to the nearest upstream curve were used. Time series data for curves that met this criteria were exam­ ined, and data were only used when the team had a high level of confidence in the reliability of the lane offset variable for the entire tangent and curve sections that were sampled, as shown in Figure 7.1. Data were ultimately available for 17 curves. Thirty­six traces were available for the inside (right­ hand curve) model, and 26 were available for the outside (left­ hand curve) model. Drivers were distributed by age and gender, as shown in Table 7.1. Variables Used for research Question 2 The conceptual model evaluates changes in driver attention and response expressed as changes in vehicle kinematics to model curve driving. The independent variables used in the models were (1) offset (in meters) and (2) the amount the driver was driving over the speed limit or curve advisory speed if present (in mile per hour). The dependent variables examined, along with a description of each, can be seen in Table 7.2. Description of analytical approach for research Question 2 Models for lane position and speed were developed for both inside (right­hand curve from the perspective of the driver) and outside (left­hand curve from the perspective of the driver). For the lane position models, a generalized least squares (GLS) model was used. A panel data model was tested with Figure 7.1. Data sampling layout for curve driving model. Table 7.1. Driver Characteristics for Research Question 2 Age Total16 to 25 26 to 50 >50 Inside curve (right-hand) Male 0 4 3 7 Female 4 1 3 8 Outside curve (right-hand) Male 0 2 2 4 Female 5 1 5 11

39 Table 7.2. Variables Used for Research Question 2 Variable Description Curve PT Factored variable that indicates the position in the curve from which data are sampled (PC, C1, C2, C3, C4, or PT) Direction Direction of the curve (0: outside/left, 1: inside/right) Radius Radius of the curve (m) Chevrons Indicator variable for chevrons (0: not present, 1: present) Rumblestrips Indicator variable for rumble strips (0: not present, 1: present) Guardrail Indicator variable for guardrail (0: not present, 1: present) RPM Indicator variable for raised pavement markings (0: not present, 1: present) AdvisSign Indicator variable for curve advisory sign (0: not present, 1: present) Nighttime indicator Indicator variable for nighttime (0: daytime or dawn/dusk, 1: nighttime) SpeedUp Speed limit in upstream (mph) SpeedDiff Speed differential between tangent and curve advisory speed (mph) Over300 Amount over the speed limit at 300 m upstream of curve (mph) Over250 Amount over the speed limit at 250 m upstream of curve (mph) Over200 Amount over the speed limit at 200 m upstream of curve (mph) Over150 Amount over the speed limit at 150 m upstream of curve (mph) Over100 Amount over the speed limit at 100 m upstream of curve (mph) Over50 Amount over the speed limit at 50 m upstream of curve (mph) Overspeed Amount over the speed limit at point in curve (mph) Speed (mph) Speed at point in the curve (mph) Offset Distance offset from centerline in points throughout curve (m) Offset300 Distance offset from centerline 300 m upstream of curve (m) Offset250 Distance offset from centerline 250 m upstream of curve (m) Offset200 Distance offset from centerline 200 m upstream of curve (m) Offset150 Distance offset from centerline 150 m upstream of curve (m) Offset100 Distance offset from centerline 100 m upstream of curve (m) Offset50 Distance offset from centerline 50 m upstream of curve (m) OffsetSD Standard deviation of offset in 300 m upstream of curve (m) Distracted200 Visual distraction in 200 m upstream of curve indicator (0: not present, 1: present) Distracted150 Visual distraction in 150 m upstream of curve indicator (0: not present, 1: present) Distracted100 Visual distraction in 100 m upstream of curve indicator (0: not present, 1: present) Distracted50 Visual distraction in 50 m upstream of curve indicator (0: not present, 1: present) Distracted Visual distraction in curve indicator (1: distraction present, 0: no distraction) Forward Forward glance at point in curve indicator (1: glance is forward, 0: glance away) SA Roadway-related glance (1: roadway-related glance, 0: otherwise) NR Non-roadway-related glance at point in curve indicator (1: present, 0: not present) NRup Non-roadway-related glance in 200 m upstream of curve indicator (1: present, 0: not present) NRcurve Non-roadway-related glance in curve indicator (1: present, 0: not present) Visibility Visibility indicator (1: low visibility, 0: otherwise) Surface Surface condition (0: dry, 1: pavement wet but not currently raining, 2: snow present, but roadway is bare) PaveCond Pavement condition (0: normal surface condition, 1: moderate damage, 2: severe damage) (continued on next page)

40 “EventID” as the individual and “Point in Curve” as the time setting. The Breusch­Pagan Lagrange multiplier test found that no panel effect was present; therefore, an ordinary least squares (OLS) model was appropriate. After running the OLS models, it was determined that there were problems with autocorrelation due to the spatial nature of the data, so a GLS model was used to correct for this. The GLS function in the NLME package of R was used to develop the models. Models were selected to minimize Akaike information criterion (AIC) and Bayesian information crite­ rion (BIC), while including significant variables from the list in Table 7.2. The correlation between the dependent variables and independent variables and the correlation between inde­ pendent variables were examined to determine which vari­ ables should potentially be included in the model. The order of autoregression parameter was tested using an analysis of variance (ANOVA) test. The correlation structure of the model took into account the grouping across each event through each unique curve. The grouping factor allows for the corre­ lation structure to be assumed to apply only to observations within the same unique event. For the amount­over­the­speed­limit model, an OLS regres­ sion model was developed. The dependent variable was the amount over the speed limit (or curve advisory speed) at point C2. Modeling the amount over the speed limit for just this point was chosen as opposed to modeling speed over the entire curve because the only significant difference in speed was found at the PT, which is not of interest in the context of speed’s role in lane­departure crashes in curves. The model was developed using the lm() function of the R software package while attempting to have the best fit. Vari­ ables were included if they were significant at the 95% con­ fidence level. Two outlier observations were not included because they skewed the fit of the model. Diagnostic tests showed that the assumptions of normality, linearity, inde­ pendence, and homogeneity were met. results for research Question 2 Four models were developed; lane position and amount of the speed limit were used as dependent variables; and models were developed for both inside (right­hand curve) and out­ side (left­hand curve) driving, because drivers tend to behave differently in each direction of curve. The dependent variable for lane position was offset of the center of the vehicle from the center of the travel lane. Positive offset is to the right, and negative offset is to the left of the center of the lane. Second­order autoregressive GLS models were developed for both lane position models. Panel models were developed for both speed models. The results of the lane position and speed­ ing models are discussed below. Lane Position Model The best fit model for lane position for right (inside) curves was developed using 216 observations and contained eight variables. The list of variables and parameter estimates is shown in Table 7.3. The model suggests that as drivers tend to the right (toward the edge line) in the upstream, the offset in the curve will also shift to the right, or near the outside of the lane. If the driver is engaged in an eyes­off­roadway distraction at a particular point in the curve, the driver’s lane position is expected to shift to the right near the outside of the lane 0.14 m at the next point. For instance, if a driver is engaged in an eyes­ off­roadway distraction at 50 m upstream, the driver’s lane position is expected to shift right 0.14 m at the PC. The model also suggests that for every year older a driver is, the driver’s lane position is expected to move toward the right 0.00345 m. Finally, the model includes indicator variables relating to the position in the curve. At position C1 (see Figure 7.1), Delineation Delineation condition (0: highly visible, 1: visible, 2: obscured) Shoulder Paved shoulder width (1: less than 1 ft, 2: 1 ft to less than 2 ft, 3: 2 ft to less than 4 ft, 4: greater than or equal to 4 ft) LargeShoulder Paved shoulder greater than or equal to 4-ft indicator (0: not present, 1: present) Gender Gender indicator (0: female, 1: male) Under25 Age under 25 indicator (0: over 25, 1: under 25) Under30 Age under 30 indicator (0: over 30, 1: under 30) Age Age of driver at time of first drive LargeVeh Large vehicle (i.e., truck or SUV) indicator (0: car, 1: truck or SUV) Table 7.2. Variables Used for Research Question 2 (continued) Variable Description

41 which is just past the point of curvature, the average position is 0.17 m to the right of the center of the lane. At position C2 the average position is 0.19 m. As the driver gets closer to the center of the curve (position C3), the average lane position is 0.40 m to the right, which is a shift of more than 0.2 m from the upstream position. Drivers then move back toward the cen­ ter of the lane at positions C4 and the PT (0.27 m and 0.18 m, respectively). As indicated, a driver’s drift to the outside lane edge near the center of the curve suggests that the driver may be most vulnerable to a right­side roadway departure near the center of the curve. These parameters support the idea that drivers do not maintain a smooth path through the curve. The first­order autoregression parameter phi was found to be 0.57808, and the second­order was –0.28316. The best fit model for lane position for left (outside) curves was developed using 156 observations and included nine vari­ ables, as shown in Table 7.4. The parameter for offset at 100 m is similar to that in the right curve lane position model, just at a slightly greater magnitude. The model suggests that if a driver tends to drive to the right of the lane center upstream of the curve, the driver will also tend to drive to the right of the lane center within the curve. When drivers engage in a non­roadway­related glance at a particular location, their lane position is expected to move to the left, or toward the centerline, by 0.13 m. At night, lane position shifts toward the left (toward the centerline) by 0.12 m, which could potentially occur because there are fewer oncoming vehicles. When a large paved shoulder (≥4 ft) is present, the model predicts that the driver will move toward the right (toward the edge line) by 0.21 m; this is expected because the driver has more space than when no paved shoulder is present. Indicator parameters for position in the curve were also included. While the parameters for indicators C4 and PT were not significant, they were still included because they give some information on the change in position throughout the curve. As drivers enter the curve and move to the center of the curve (positions C1 to C3, as shown in Figure 7.1), they tend to be positioned about 0.16 m to 0.21 m to the left of the center of the lane (toward the centerline). As drivers move to the end of the center of the curve (position C4 and the PT), they move to the right toward the center of the lane. This sug­ gests that drivers may be most likely to cross the roadway cen­ terline as they enter the curve. Speed Model The amount a driver was over the advisory speed if present or posted tangent speed if not present was modeled at point C2 using OLS. The best fit model had an adjusted R2 value of 0.741 (n = 60) and five variables. Speed model variables are shown in Table 7.5. Model results show that for every 1.6 km/h (1.0 mph) over the speed limit a driver is traveling at 100 m upstream of the curve, the amount over the speed limit at point C2 is expected to increase by 1.1 km/h (0.7 mph). This result is expected Table 7.3. Significant Variables for Right Curve Lane Position Model Variable Parameter Estimate p-Value Constant -0.22185 0.0005 Offset at 100 ft upstream of curve 0.36714 0.0000 Distracted at the previous point in the curve or upstream indicator (0: not distracted, 1: distracted) 0.13592 0.0500 Driver’s age (years) 0.00345 0.0001 C1 position indicator (0: not C1, 1: C1) 0.16931 0.0001 C2 position indicator (0: not C2, 1: C2) 0.18865 0.0012 C3 position indicator (0: not C3, 1: C3) 0.39609 0.0000 C4 position indicator (0: not C4, 1: C4) 0.26790 0.0000 PT position indicator (0: not PT, 1: PT) 0.17682 0.0020 First-order autoregression disturbance parameter (phi 1) 0.57808 Second-order autoregression disturbance parameter (phi 2) -0.28316 Number of observations 216

42 because drivers who are traveling over the speed limit in the tangent are also likely to speed within the curve. Speeds are expected to be 2.8 km/h (1.7 mph) slower at nighttime than during the day. Additionally, the model suggests that those who drive a truck or SUV are expected drive 2.1 km/h (1.3 mph) faster than those who drive a passenger vehicle. The model also found that for every additional 10 years in age for a driver, speed decreases by 0.9 km/h (0.5 mph). Finally, the model suggests that if drivers are engaged in a non­roadway­related glance at point C2, they are expected to be driving 5.3 km/h (3.3 mph) slower than if they were glancing at the roadway. Summary and Implications The objective of Research Question 2 was to define normal curve driving. Understanding how a driver normally negotiates a curve during various situations provides insight into not only how characteristics of the roadway, driver, and environment potentially influence how a driver drives, but also the areas that Table 7.4. Significant Variables for Left Curve Lane Position Model Variable Parameter Estimate p-Value Constant 0.00067 0.9904 Offset at 100 ft upstream of curve 0.44811 0.0002 Nonroadway glance at point in curve indicator (0: roadway glance, 1: nonroadway glance) -0.13466 0.0193 Night indicator (0: daytime, 1: night) -0.12283 0.0155 Paved shoulder greater than 4 ft indicator (0: paved shoulder less than 4 ft, 1: paved shoulder ≥ 4 ft) 0.21273 0.0006 C1 position indicator (0: not C1, 1: C1) -0.17691 0.0014 C2 position indicator (0: not C2, 1: C2) -0.20758 0.0044 C3 position indicator (0: not C3, 1: C3) -0.16169 0.0304 C4 position indicator (0: not C4, 1: C4) -0.02272 0.7495 PT position indicator (0: not PT, 1: PT) 0.05718 0.4071 First-order autoregression disturbance parameter (phi 1) 0.49063 Second-order autoregression disturbance parameter (phi 2) -0.26283 Number of observations 156 Table 7.5. Significant Variables for Speed Model Variable Parameter Estimate p-Value Constant 3.70299 <0.001 Amount over the speed limit at 100 m upstream of curve 0.70772 <0.001 Driver’s age (years) -0.05340 <0.001 Night indicator (0: daytime or dusk, 1: nighttime) -1.73462 0.028 Vehicle type (0: car, 1: truck or SUV) 1.30152 0.029 Non-roadway-related glance at current point indicator (0: roadway-related glance, 1: non-roadway-related glance) -3.32218 0.037 Number of observations 60 Adjusted R2 0.741

43 can lead to roadway departures. Knowing how much drivers normally deviate in their lane, as well as how they choose their speed, could potentially have implications on policy or design. Conceptual models of curve driving were developed to assess changes in lane position and speed as the driver negoti­ ates the curve. Understanding how a driver normally negoti­ ates a curve during various situations provides insight not only into how characteristics of the roadway, driver and envi­ ronment potentially influence driving behavior, but also into areas that can lead to roadway departures. Additionally, the model indicates boundaries for normal driving. Originally, the intent of answering this research ques­ tion was to use this information to identify events of interest (nonnormal driving) to help establish boundaries between noncrash roadway departure events for Research Question 3. This was not possible because many traces did not have lane position of sufficient reliability, and Research Question 3 required a larger sample size than the other research questions. Data for several positions upstream and along the curve were sampled from the time series data. Models were devel­ oped for lane position and speed for both inside (right­hand curve from the perspective of the driver) and outside (left­ hand curve from the perspective of the driver), resulting in four models. Lane position was modeled as the offset of the center of the vehicle from the center of the lane. Models were developed using GLS. Summary of Results Results indicate that lane position within the curve is influ­ enced by lane position upstream of the curve. The models developed for offset of lane centerline in this study found that drivers who were distracted or glanced away from the road­ way tended to shift away from the center of the lane. When driving on the inside of the lane, a driver who was distracted at a particular point within the curve tended to shift 0.14 m to the right by the next point in the curve. When driving on the outside (left­hand curve), a driver who engaged in a non­ roadway­related glance at a particular location within the curve was expected to move to the left, or toward the center­ line, by 0.13 m at that same point. This confirms the role of distraction in lane keeping. The models also found that drivers on the inside of a curve tended to move more to the right at the center of curve, while drivers on the outside of a curve were at the furthest point from the centerline at the beginning of the curve. This sug­ gests that drivers may be particularly vulnerable to roadway departures at certain points in the curve negotiation process. Additionally, the lane offset models indicated that age and nighttime are factors in driver lane position. The model for speeding in the curve found that if drivers are speeding in the upstream, they will also speed in the curve. Drivers of SUVs and pick­up trucks travel on aver­ age 2.1 km/h (1.3 mph) faster than drivers of passenger vehicles. Speeds were predicted to be 0.9 km/h (0.5 mph) lower for each additional 10 years in age for a driver, and drivers who were engaged in a non­roadway­related glance were expected to travel 5.3 km/h (3.3 mph) slower than drivers who were not engage in a non­roadway­related glance. This suggests that drivers whose attention is focused away from the road­ way do not maintain longitudinal control. Implications for Countermeasures Lane position varies as a function of position within the curve. On the inside of a curve lane, position offset is greatest at the center of the curve. For the outside of the curve lane, position offset is the largest at the beginning of the curve. Additionally, drivers who engaged in eyes­off­roadway dis­ tractions tended to shift right of the center of the lane on the inside of the curve. Both factors indicate that drivers may be more vulnerable to a lane departure at certain points within the curve. As a result, countermeasures such as rumble strips, paved shoul­ ders, and high­friction treatments may ameliorate the conse­ quences of variations in lane position through the curve. Lane position offset is greater for the outside of the curve during nighttime driving, which suggests that better delinea­ tion of curves (edge lines, post­mounted delineators, chev­ rons) may aid drivers in nighttime curve driving. The models also confirm that drivers who speed upstream are likely to speed within the curve, which suggests that countermeasures that reduce speeds upstream will calm speeds within the curve. Limitations The main limitation of this analysis was sample size. Reliable offset data were only available in a subset of the vehicle traces that were reduced. As a result, the number of driver types and roadway features that could be modeled was limited. Conse­ quently, the results are not transferable to all curves or situa­ tions. Adding more data to these models may draw out more relationships or strengthen those already found. A more robust data set could also allow for a mixed effects model to be per­ formed, which would allow the findings to be applied toward more curves than those used in the study. Although the models provided information about factors that result in greater deviation within the lane or higher speeds, the models did not draw correlations between these two factors and increased roadway departure crash risk. It is only assumed that countermeasures that improve lane position or reduce speeds will also reduce roadway departure crashes.