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

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29 C h a p t e r 6 This chapter discusses the first research question: What defines the curve area of influence? Drivers begin to react to a curve at some distance upstream. This is expected to vary according to curve geometry, sight distance, and countermeasures present. Understanding where drivers begin to react to the curve is important for placement of traffic control and countermeasures. A better understand- ing of where drivers begin to react to a curve can help agen- cies determine the optimal placement of advance signing and other countermeasures. Currently, placement of advisory signing along rural curves is primarily based on posted or 85th-percentile speeds and the amount of deceleration necessary for curve negotiation, fol- lowing guidelines in the Manual on Uniform Traffic Control Devices (MUTCD), Chapter 2 (Federal Highway Administra- tion 2009). When no deceleration is necessary, the distance var- ies from 31 m (100 ft) at 56 km/h (35 mph) to 122 m (400 ft) at 97 km/h (60 mph). Distances increase when speed reduction and lane changing in heavy traffic are expected. Given that appropriate driver response upstream of a curve is necessary for proper speed selection and curve negotiation, defining the curve area of influence was necessary to determine how much data upstream of the curve should be included in the present analyses. The objective of Research Question 1 was to identify where drivers begin reacting to a curve. A better understanding of where drivers begin to react to a curve can help agencies better determine placement of advance signing and other counter- measures. Research Question 1 was also used to indicate the curve area of influence for Research Questions 2, 3, and 4. Data Sampling and Variables Used for research Question 1 Use of eye tracking would have been ideal to determine where drivers were looking and noticing curves. However, eye track- ing was not possible with the video data, and driver glance location could only be identified for general directions (e.g., left, right, steering wheel). As a result, glance location could not be pinpointed with sufficient accuracy to determine whether a driver noticed traffic control or roadway countermeasures. Therefore, vehicle kinematic data (i.e., braking or changes in speed) were the only method to assess at what point drivers began reacting to the curve. Analyses in Phase 1 indicated that pedal position, speed, and steering wheel position could be used jointly to indicate the point at which a driver began react to the curve. Braking was only present in a few events and was therefore not used. After data were received for Phase 2, it became evident that steering wheel position was not universally recorded. As a result, change in speed and change in pedal position were the variables used to indicate where drivers began reacting to the curve. Time series data were used for Research Question 1. Data may be output at different resolutions by the different sensors but are usually aggregated to 10 Hz (0.1-s intervals). Addi- tional variables, such as vehicle position relative to the curve, were calculated and reported at the same resolution. Changes in pedal position and speed were smoothed over 0.5-s intervals and were calculated for each row to minimize the impact of noise using a moving average smoothing method. An example of time series data was shown in Table 3.2. Speed was reported at 0.1-s intervals for the majority of the traces. Pedal position was also usually available but in many cases was reported at less frequent intervals (e.g., reported at 0.6- or 0.8-s intervals), which was too coarse for the models to detect changes. Consequently, only traces that had been reduced for the initial data request (about 200) that had both speed and pedal position reported at 0.1-s intervals were used in the analyses. Additionally, only curves with a minimum distance of 400 m (1,312.3 ft) to the nearest upstream curve were used. Analyses in Phase 1 had suggested that drivers begin reacting to the curve within 200 m (656 ft), so provision of 400 m (1,312.3 ft) upstream allowed sufficient distance upstream of the expected Analysis for Research Question 1

30 reaction point to represent normal driving. Data were extracted for each curve of interest for a distance of 400 m (1,312.3 ft) upstream and through the curve. Sample size was limited by the constraints described above. The analyses included 127 traces across 36 curves in Indiana, New York, and North Carolina. Curve radius varied from 117 m to 7,106 m (383.9 ft to 23,313.7 ft). Three curves had chevrons, four had W1-6 signs, none had rumble strips, five had guard- rails, 21 had raised pavement markings, and 16 had curve advisory signs. Methodology for Defining Curve area of Influence The point at which significant pedal position changes occurred was obvious in some traces, as shown in Figure 6.1, which shows pedal position for two traces (two drivers). In other cases, sufficient noise was present for pedal position and steer- ing wheel position, so it was more difficult to identify the point of reaction, as shown in Figure 6.2. A change point model was used to determine where drivers were reacting to the curve. A separate model was fit to each curve for each event using time series data. Change point mod- els were fit using the statistical package R, which uses a regres- sion model based on Muggeo (2008). The form of the model is as follows: *0 1 2Y D D D( )= β + β + β − where Y = the dependent variable for each model, which was either speed in meters per second or gas pedal position; D = distance from the point of curvature, in meters; and D* = change point (the distance at which the driver reacts to the curve). Note that distances are measured backwards from the point of curvature (D = 0), so all distances for this part of the analysis are negative. A change point model was selected because it could identify the point at which speed or pedal position changed significantly from upstream driving. The third parameter of the model, b2, represents the strength of the reaction. If b2 is not significantly different from zero, this indicates that the driver did not react in a noticeable way to the curve. Thus, for this model the researchers were most interested in the values of b2 and D*, because D* indicates the point at which the driver reacted to the curve and b2 indicates how strong that reaction was. The identified reaction points are only meaningful if the strength of the reaction, the value of b2, is significantly different from zero. So, the estimated b2 value for each model was tested against the hypothesis that b2 = 0. Models were developed independently for speed and pedal position for each curve, for travel in the direction inside of the curve and outside of the curve. The reaction distance was then compared to MUTCD sign placement values. Figure 6.1. Change in pedal position for two drivers (Florida Curve 101).

31 A second model was developed for traces for 11 curves in Indiana for which multiple drivers were available. A Bayesian hierarchical change point model is as follows: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) = β + β + β − + β + β β β τ = β β φ = β τ φ * , accounts for variability among drivers, for 0, 1, 2 , accounts for variability between curves, for 0, 1, 2, 3, 4 0, 100 noninformative prior 0.01, 0.01 noninformative hierarchical prior 0.01, 0.01 noninformative hierarchical prior 0 1 2 3 4 2 2 2 2 Y D D D R C Normal k Normal k Normal Inverse Gamma Inverse Gamma ij ij i i k k k k k k k k k ij ij ij ij i i ∼ ∼ ∼ ∼ ∼ where i indexes the curve; j indexes the driver; and Ri and Ci are the radius and travel direction of curve i, respectively. results for research Question 1 Speed Model The fitted change point models with speed in meters per sec- ond as the dependent variable are plotted for each curve, as shown in Figures 6.3 to 6.5. A model was developed for each trace for each curve. Model results are provided in Appendix C. Results are shown graphically in Figures 6.3 to 6.5 and are grouped by state and by curve and direction of travel (inside versus outside of the curve). Traces for many curves have similar reaction points, as indicated by the slope of the line changing at about the same point, such as curves IN44Ain and IN44Jout. Others, however, have distinctly different reaction points, as shown for curves IN13Ain and IN13Aout. The average point at which drivers reacted for all curves was 164 m (538.1 ft) upstream of the curve. Results were aver- aged by curve radius, as shown in Table 6.1. When the models were tested for significant reactions, 96 of the 127 models were found to have significant driver reactions at the 95% confi- dence level, as shown in Appendix C. Pedal Position Model Change point models were also developed using pedal posi- tion as an indicator of driver response. This variable has no units, but is a measure of how far the driver is pushing down on the gas pedal. If the value increases, the driver is increasing pressure on the pedal, and if the value decreases, the driver is decreasing pressure (letting up) on the pedal. For the same 127 traces across 36 curves in Indiana, New York, and North Carolina, the fitted change point models show pedal position as the dependent variable. Model results are provided indi- vidually in Appendix C. Results are plotted graphically in Fig- ures 6.6 to 6.8 and are grouped by state, curve, and travel direction (inside versus outside of the curve). As noted, some of the curves have very similar reaction points for all events, which can be seen in curves IN13Aout and IN44Iout. Others, however, have very separated reaction points (e.g., curves IN44Ain and IN44Dout). Again, the values of b2 and D* are of the most interest. The furthest reaction point was approximately 488 m (1,601.1 ft) Figure 6.2. Change in pedal position for one trace in which change is not obvious.

32 Figure 6.3. Fitted speed models for Indiana curves. Figure 6.4. Fitted speed models for New York curves.

33 before the point of curvature, and the closest reaction point was approximately 13 m (42.7 ft) before the point of curva- ture, with the mean reaction point about 179 m (587.3 ft) before the point of curvature. The estimated b2 value for each model was again tested against the hypothesis that b2 = 0, and 99 of the 127 models were found to have significant driver reactions at the 95% confidence level. The average point at which drivers reacted for all curves was 180 m upstream of the curve, which was similar to the results for the speed models. Results were averaged by curve radius, as shown in Table 6.2. Results for individual models are shown provided in Appendix C. Table 6.1. Speed Change Points Results by Curve Radius Radius in Meters (feet) Average Change Point in Meters (feet) Number of Curves <1000 (3281) -142.9 (-468.8) 4 1000 to <1500 (3281 to <4921) -146.1 (-479.3) 7 1500 to <2000 (4921 to <6562) -193.2 (-633.9) 11 2000 to <2500 (6562 to <8202) -191.1 (-627.0) 6 ≥2500 (≥8202) -149.8 (-539.7) 8 Figure 6.5. Fitted speed models for North Carolina curves. Results for Bayesian Model The Bayesian model was only fit to a subset of the data: 11 curves in Indiana for which there was adequate repetition of drivers across curves. This model is an improvement on the current model because it is able to account for the individual differences among drivers, as well as the differences between curves. This model also allows the prediction of appropriate reaction points for other curves not included in the study, which could aid in deciding where to place chevrons and/or dynamic speed feedback display units to lower crash incidents on rural curves. After accounting for the radius of the curve, the travel direc- tion of the curve, and the variability among drivers, all curves were found to have about the same reaction point, approxi- mately 105 m (344 ft) upstream of the curve. The 95% poste- rior credible interval for this estimate is from 136 m to 64 m (446 ft to 210 ft) upstream of the curve. The exact reaction point for each curve changes with curve radius, and curve direction is given by the estimates of b3 and b4. The estimate of b3 is -0.000872, with a posterior 95% credible interval of (-0.00143, -0.000284). So, for every addi- tional 100 m (328.1 ft) in the radius of the curve, the reaction point moves back from the point of curvature by 0.0872 m (0.29 ft). The estimate of b4 is -1.991, with a posterior 95% credible interval of (-3.112, -0.73). The curve directions

34 Figure 6.7. Fitted pedal position models for New York curves. Figure 6.6. Fitted pedal position models for Indiana curves.

35 were coded as 0 for inside and 1 for outside, so this estimate indicates that the reaction point moves on average about 2 m (6.6 ft) further from the point of curvature when the driver is traveling on the outside of the curve. Summary and Discussion The objective of Research Question 1 was to identify the point at which drivers begin reacting to a curve. A better understand- ing of where drivers begin to react to a curve can help agen- cies better determine placement of advance signing and other countermeasures. Research Question 1 was also used to indicate the curve area of influence for Research Questions 2, 3, and 4. Key Findings Time series data were modeled using regression and Bayesian analysis. The point at which speed and pedal change are sig- nificantly different from that of upstream driving was identi- fied. Results indicate that, depending on the radius of the curve, drivers begin reacting to the curve 164 m to 180 m (538.1 ft to 590.6 ft) upstream of the point of curvature. Results did suggest that drivers begin reacting to the curve sooner for curves with larger radii than for curves with smaller radii, as shown in Table 6.3. This was unexpected because sharper curves are more likely to have advance signing, chev- rons, or other countermeasures that have the express purpose Figure 6.8. Fitted pedal position models for North Carolina curves. Table 6.2. Pedal Position Change Points Results by Curve Radius Radius in Meters (feet) Average Change Point in Meters (feet) Number of Curves <1000 (3281) -137.4 (-450.8) 4 1000 to <1500 (3281 to <4921) -163.9 (-537.7) 7 1500 to <2000 (4921 to <6562) -198.1 (-649.9) 11 2000 to <2500 (6562 to <8202) -205.6 (-674.5) 6 ≥2500 (≥8202) -186.0 (-610.2) 8 Table 6.3. Average Change Point Radius in Meters (feet) Average Change Point in Meters (feet) Pedal Position Speed <1000 (3281) -137.4 (-450.8) -142.9 (-468.8) 1000 to <1500 (3281 to <4921) -163.9 (-537.7) -146.1 (-479.3) 1500 to <2000 (4921 to <6562) -198.1 (-649.9) -193.2 (-633.9) 2000 to <2500 (6562 to <8202) -205.6 (-674.5) -191.1 (-627.0) ≥2500 (≥8202) -186.0 (-610.2) -149.8 (-539.7)

36 of getting a driver’s attention. Additionally, drivers traveling at appropriate speeds do not need to reduce speed to the same extent on curves without advisory speeds as for curves where deceleration is necessary. There may be several reasons for the unexpected results. First, countermeasures that simply warn drivers of an upcom- ing curve may not be sufficient to change driver behavior. Better delineation of the curve may be more effective in pro- viding the appropriate roadway cues. Most of the curves with smaller radii had some type of advance warning, but only three had chevrons, which are highly visible in all environ- mental conditions. Three additional curves had raised pave- ment markings (RPMs), but RPMs are not as obvious during daytime conditions as during nighttime and wet weather conditions. Due to the sample size available, it was not possi- ble to draw relationships between reaction point and presence of a specific countermeasure. It is possible that driver reaction for sharper curves is more pronounced, and as a result, the models were better able to identify the reaction point. Another explanation for the unex- pected results is that drivers may indeed be reacting to advance signing and delineation and are more gradually slowing than for curves with larger radii. Sight distance may also be an issue for sharper curves. Implications for Countermeasures The MUTCD (Federal Highway Administration 2009) suggests placement of warning signs based on posted or 85th-percentile speed, the driver’s ability to decelerate to the posted advisory speed for the condition, and an assumed legibility distance of 76 m (250 ft). Sign placement for posted/85th-percentile speeds from 72 km/h to 89 km/h (45 mph to 55 mph) range from 31 m to 99 m (100 ft to 325 ft). As a result, the point at which a driver is able to view a sign (assuming favorable visibility and sight distance) is 107 m to 175 m (350 ft to 575 ft). It should be noted that driver reaction point may be influ- enced by signs, and as a result, some correlation exists between presence of signs and reaction point. However, it was assumed that a warning sign only provides information to the driver and does not in and of itself cause the driver to react sooner. The average point at which drivers begin reacting to the curve is summarized by curve radius in Table 6.3. This repre- sents the reaction point for drivers who successfully negotiated the curve. Given that warning signs are only likely to be present for curves with smaller radii, sign placement falls within the reaction distance, suggesting that sign placement distances are appropriately set. The results showing that drivers react sooner to curves with larger radii indicates that advisory signs and advisory speeds may not be sufficient to alert drivers to the upcoming curves. Countermeasures that provide better curve delineation, such as chevrons, may provide better cues to drivers so that they can gauge the sharpness and respond appropriately. Limitations One of the major limitations of this analysis is that driver glance location could not be used to detect driver response to an upcoming curve. Braking and steering may have provided additional insight but were not sufficiently available to include. As a result, the models depended on change in speed and pedal position to detect reaction point. The major limitation to these speed and pedal position analy- ses is that, even with smoothing, there was a significant amount of noise. As a result, it was difficult to detect reaction point. Sample size was also a limitation in this analysis. The sam- ple size was limited by the number of traces with reliable pedal position values that were available in the data that could be reduced within the project constraints. If additional data were included, the models might be able to relate reaction point to countermeasures.