Evaluation of Data Needs, Crash Surrogates, and Analysis Methods to Address Lane Departure Research Questions Using Naturalistic Driving Study Data (2011)

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A P P E N D I X A Methodology for Extraction of Data Elements from the UMTRI Naturalistic Driving Study Data SetThis appendix includes description of the methodology to extract variables necessary to answer lane departure research questions using the UMTRI naturalistic driving study data set. The focus of the analysis is lane departures on rural, two-lane roadways. All the data were extracted and reduced manually, since the team was exploring and evaluating what was available with the data. This took a tremendous amount of resources. Once researchers spend some time familiarizing themselves with the data in the full-scale study, it is expected that methods can be developed to automate some of the data extraction. The data sets used are described in detail in Chapter 3. Data Preparation The UMTRI data were provided in the form of continuous vehicle data. Each row of data represented 0.1 s of driving. Vehicle data were provided by vehicle alert type as indicated in the section “University of Michigan Transportation Research Institute Field Operational Test In-Vehicle Data” at the begin- ning of Chapter 3. The road departure crash warning (RDCW) system included six levels of alerts to indicate to the driver that he or she was about to leave his or her lane or was traveling too fast on a curve. The alerts included a right- and left-lane depar- ture cautionary alert, right- and left-lane departure imminent alerts, cautionary curve speed warning, and imminent curve speed warning. A seventh designation was used to indicate that a vehicle was negotiating a curve, but no alert has been included for this. Data were provided on 44 drivers. Data were divided by alert type. Over 2,000 alerts/curves were received. Continuous data were provided, with a resolution of 10 Hz (one row rep- resents 0.1 s). A total of 1,506,525 rows of data were received. Data were provided for 30 s before an alert was recorded to approximately 30 s after (called a trace). Instances of a vehicle negotiating a curve were also provided as samples109of regular driving and also included approximately 60 s of data (approximately 600 rows per alert/curve). The data- base contained a number of data fields (columns) with data from the instrumentation system, such as lateral acceleration and forward speed. The data corresponding to each alert is referred to as a “vehicle trace.” The data also contained a number of columns that represent data from sources other than the instrumentation system, such as static driver char- acteristics (age, gender) and roadway variables (lane width, road class). A large amount of time was spent reviewing the vehicle trace data set to determine what was included and how to link the UMTRI database and forward video data. Latitude and longitude were provided for each row of data, and geographic files were created for each vehicle trace using ArcMap. Each UMTRI vehicle trace was overlaid with aerial imagery, and the roadway type identified from the aerial image was matched to individual vehicle traces. Vehicle location (e.g., tangent, curve, freeway ramp) was determined and mapped to the corresponding vehicle rows. Vehicle data in the vicinity of a major intersection where the vehicle would have stopped or slowed significantly were identified and tagged. Data around intersections where the vehicle stopped or slowed significantly were not included in the final analysis. Overlap in vehicle traces was also identified and removed. The team found significant overlap in the UMTRI vehicle traces. This is due to the manner in which the data were queried. For instance, UMTRI extracted data on curves, so when several curves were in a row, a vehicle trace was extracted for each curve. This resulted in several vehicle traces with over- lapping data (see Figure A.1). The data for the overlapping areas were for the same vehicle, trip, and times. It was neces- sary to identify overlaps so that the same data would not be used twice in the analysis.The rural designation used by UMTRI was for data collected in locations where the population was less than 50,000. This resulted in vehicle traces located in developed

110Image source: Esri. © 2010 i-cubed. Vehicle trace source: UMTRI. Figure A.1. Overlapping vehicle traces.areas. The team identified and removed vehicle traces where the activity occurred within an incorporated area or in an area with significant development along the roadway. Only regular rural driving was desired, and areas with a large amount of development would result in different driving patterns. A large number of vehicle traces that indicated a driver was negotiating a curve turned out to be either a vehicle turning at an intersection or a vehicle turning off of or onto a roadway. Occurrences of these types were indicated. If the majority of the vehicle trace was regular, uninterrupted rural driving, the nonintersection or nonturning portion of the trace was retained. When the majority of the vehicle trace was turning activity, the trace was not included. Preparation of the data for further analysis required a sig- nificant amount of manual data reduction. Additionally, the lane tracking system used in the RDCW did not perform well on unpaved surfaces. As a result, the team decided to focus on rural, two-lane, paved roadways. All resulting analyses were for this type of roadway. Available List of Variables Included in Analysis and Methodology to Extract Additional Variables The following is a list of variables available in the UMTRI data or extracted to be included in the analyses of lane departures using the naturalistic driving study data. The variables are summarized by category: general, driver, vehicle, roadway, environmental, and exposure.General Variables Included in the UMTRI Data Set The following general data fields were included in the UMTRI database. They were not included as variables in any of the analyses but were used in the extraction of other data. • Time: In centiseconds (cs) since DAS started. Indicates time into the trip. It was used to identify alert times, identify overlap between vehicle traces, flag the beginning and end of events, determine how far into the trip an event occurred, and was used as an identifying feature. It was also used to correlate forward video images to vehicle traces. • Starttime: Indicates the time an alert identified by UMTRI started. Time in cs since DAS started. • Endtime: Indicates time an event identified by UMTRI ended. Time in cs since DAS started. • EventID: Indicates the type of alert that was flagged for the vehicle trace. The alert was defined by the UMTRI FOT. This information was used to flag potential lane departures as defined by the UMTRI researchers. Events were defined differently for the research described in this report. This information was only used as a starting point to define events. The data field EventID used the following convention: – 1: LDW Cautionary Left; – 2: LDW Cautionary Right; – 3: LDW Imminent Left; – 4: LDW Imminent Right; – 5: Curve Speed Cautionary; – 6: Curve Speed Imminent; and – 7: Negotiating Curve (this indicated the presence of a curve but in most cases represented normal driving).

111• LDWBoundaryRight and LDWBoundaryLeft: Represent the type of lane line to the left or right of the vehicle’s present lane. This information was used by the UMTRI system to determine position and offset within a lane. Lane lines were indicated as follows: – 0: missing; – 1: dashed; – 2: solid; and – 3: virtual. • Latitude and Longitude: In degrees. Both were used in identifying vehicle position for each time interval and in creating vehicle traces in Esri’s geographic information system package, ArcMap, as shown in Figure A.1. • Heading: In degrees. Indicates GPS heading for each time interval. • Radius: In meters. The radius of curvature was calculated from the lane departure warning system. This data field was subsequently determined to be inaccurate, so the radius of curve was then calculated from aerial imagery by the CTRE team. • ThruLanes: Indicates the number of through lanes. This variable was used to identify vehicle traces on two-lane roadways. • ShoulderLeft and ShoulderRight: In meters. These vari- ables indicate shoulder width. In all cases, their values were recorded as 5 m. These values were subsequently determined to be inaccurate, so actual shoulder widths were then deter- mined and extracted using the forward images. Driver Variables The following driver variables were available with the original data set or were extracted from the various data sets.• Driver age: In years. Provided with data set. • Driver gender: Provided with data set; 1 = male, 2 = female. • Trip number: Provided with data set. The number of trips previous to and including the current trip. • Aggression_Accel: Percentage. This variable reflects aggres- sive driving. It is defined as the percentage of time a specific driver exceeds a set acceleration level. The acceleration level is specific to the facility (e.g., two lane, freeway, intersection). The acceleration level can be determined by developing a distribution of accelerations (in m/s2) for all drivers in the data set where vehicle activity is on two-lane rural roadways and the data did not include stopping or starting at intersections. The threshold will be set once all data have been reduced for all drivers. Acceleration for each time interval is available from the variable Ax. Figure A.2 shows the acceleration distribution for Drivers 6 and 12. Acceleration should be separated by positive and negative acceleration.(a) (b) Figure A.2. (a) Distribution of deceleration and (b) acceleration (m/s2) for Drivers 6 and 12.• OvrSpd5 and OvrSpd10: Percentage. These variables reflect aggressive driving. They are defined as the percentage of time a specific driver exceeds the posted speed limit by 5 or 10 mph, respectively. The percentage of time driver k exceeds the speed limit by i mph was calculated using Equation A.1: This reflects driving traces included in the analysis of two-lane roadways. Records with missing data were not included in the analysis. PerOverSpeed number of records where spee ik = d for driver mph over speed limit Total k i≥ number of records for driver A k ( . )1

112• OvrCurveSpd5 and OvrCurveSpd10: Percentage. These variables reflect aggressive driving. They are defined as the percentage of time a specific driver exceeds the advisory curve speed limit by 5 or 10 mph (when there is a curve advisory). The percentage of time driver k exceeds the curve advisory speed limit by i mph was calculated using Equation A.2: PerOverCurveSpeed number of records where ik = speed for driver mph over curve advisok i≥ ry speed limit Total number of records for driver where there are curve speed limit k advisories A( . )2Summary Statistics for Aggressive Driving Variables Several variables were created to assess a measure of aggressive driving. Acceleration distributions were created for each driver for nonevent (normal) data. Table A.1 shows the acceleration summary statistics for individual drivers. The data represent driver accelerations during nonevents (normal driving). As shown, individual driver characteristics vary. Figures A.3 and A.4 provide box plots showing ranges of driver accelera- tion characteristics.Dr6 Dr8 Dr12 Dr14 Dr16 Dr17 Dr18 Dr24 Min: −2.59 −2.96 −1.20 −0.47 −0.93 −2.11 −2.27 −2.23 Mean: −0.07 −0.09 −0.02 0.14 0.01 −0.03 −0.02 −0.02 Max: 1.25 1.71 1.17 0.94 2.09 1.96 1.52 1.29 Std Dev. 0.37 0.53 0.27 0.31 0.28 0.34 0.42 0.38 Dr28 Dr35 Dr48 Dr51 Dr59 Dr60 Dr64 Dr85 Min: −2.74 −2.36 −2.44 −2.61 −3.08 −2.78 −2.32 −2.67 Mean: 0.00 −0.03 −0.07 −0.11 −0.09 −0.07 −0.03 −0.03 Max: 1.76 2.09 1.19 1.22 0.74 1.88 1.26 2.15 Std Dev. 0.35 0.40 0.33 0.40 0.49 0.54 0.52 0.43 Table A.1. Acceleration Statistics for Individual Drivers for Two-Lane Rural Paved RoadsFigure A.3. Box plots showing acceleration ranges for Drivers 6, 8, 12, 14, 16, 17, 18, 24.Table A.2 provides a summary of the percentage of time each driver travels over the posted speed limit by 5 or 10 mph, or the curve advisory speed limit by 10 or 15 mph. Cells shown as NA indicate curves with no advisory speed limits for the

113Figure A.4. Box plots showing acceleration ranges for Drivers 28, 35, 48, 51, 59, 60, 64, 85.Posted Speed Limit Advisory Speed Over Over Over Driver 5 mph 10 mph 10 mph OvrAdv15 6 0.0% 0.0% NA NA 8 49.0% 7.0% NA NA 12 8.0% 0.0% 83.0% 11.0% 14 36.0% 5.3% NA NA 16 1.2% 0.0% 31.4% 14.1% 17 0.9% 0.0% 2.3% 0.0% 18 12.1% 6.0% 41.7% 27.1% 24 36.0% 3.0% 78.0% 12.0% 28 90.2% 81.8% 100.0% 45.4% 35 21.9% 2.1% 41.1% 16.0% 48 25.0% 3.0% 75.0% 47.0% 51 13.2% 0.0% NA NA 59 8.5% 0.0% 89.0% 7.5% 60 41.8% 15.0% 63.7% 25.0% 64 55.5% 11.1% 61.1% 28.4% 85 25.0% 3.0% 75.0% 47.0% Table A.2. Percentage of Time Driver Spends Over Posted or Advisory Speed Limitdriver or the advisory speed was unknown. As indicated, drivers regularly travel over the posted and advisory speed limits but do so at different frequencies. Driver 6 rarely trav- eled over the posted speed limit and Driver 17 rarely traveled over either the posted or advisory speed limit. In contrast, Driver 28 traveled over the posted speed limit by 5 or 10 mph most of the time, exceeded the advisory speed on curves by 10 mph all of the time, and exceeded the advisory speed by 15 mph 45% of the time. Vehicle Variables All vehicles in the UMTRI data set were of the same type. Thus, no individual vehicle characteristics, such as vehicle height, were considered. The following vehicle variables were included in the data set or were extracted: • Speed: In meters per second (m/s). Provided with the data set, this variable indicates forward (longitudinal) vehicle velocity for each time interval. • LateralSpeed: In m/s. Provided with the data set, this variable indicates lateral vehicle velocity for each time interval. • Ax: In meters per second squared (m/s2). Provided with the data set, this variable indicates forward (longitudinal) vehicle acceleration for each time interval. Deceleration is defined as negative acceleration. • Ay: In m/s2. Provided with the data set, this variable indi- cates lateral vehicle acceleration for each time interval. Deceleration is defined as negative acceleration.

114• Brake: Provided with the data set, this is a categorical variable that indicates whether the brake was engaged, where 0 = not engaged and 1 = engaged. • Engaged: Provided with the data set, this is a categorical variable that indicates whether cruise control was engaged, where 0 = off and 1 = on. • Roll: In degrees. Provided with the data set, this variable indicates degrees of roll for each time interval. • RollRate: In degrees per second (deg/s). Provided with the data set, this variable indicates roll rate for each time interval. • PitchRate: In deg/s. Provided with the data set, this vari- able indicates pitch rate for each time interval. • YawRate: In deg/s. Provided with the data set, this variable indicates pitch rate for each time interval. • AmrRight and AmrLeft: In meters. Provided with the data set, these variables indicate distance to the nearest object to the right or left, respectively, for each time interval. • TravelDirection: Determined from the time stamp and the aerial image (categorical). This variable indicates the primary direction of travel, where NB = northbound, SB = south- bound, NEB = northeast bound, and so forth. Roadway Variables The following variables are those that relate to the roadway and were either available with the UMTRI data set or were extracted from variables or other data sets. • LaneWidth: In meters. Provided with the data set, this variable records the lane width for every time interval and was calculated within the instrumentation package based on the presence of left and right lane lines. Since lane width can vary from time interval to time interval, lane width was averaged across all intervals for each vehicle trace according to Equation A.3. where LaneWidthAvgk = average lane width for the travel lane calculated for each vehicle trace, LaneWidthi = lane width for time interval i, and Nk = number of time intervals in vehicle trace k. • RoadType: Determined from aerial imagery (categorical). Vehicle traces were overlaid with aerial imagery and time intervals were coded according to the corresponding road- way type. A single trace could consist of vehicle activity on several different roadway types. Areas around intersections were only designated as “intersection” when the vehicle LaneWidthAvg LaneWidth Ak i k = Σ N ( . )3would have to stop or slow down to yield right-of-way. Time intervals for intersections where the vehicle was not presented with any traffic control were coded as the regu- lar roadway type (e.g., two-lane undivided). The variable RoadType was compared against the variable RoadClass included with the data, but was more descriptive. RoadType was designated using the following conventions: – 1: Two-lane undivided (one lane each direction); – 2: Four-lane undivided; – 3: Six-lane undivided; – 4: Four-lane divided (two lanes each direction); – 5: Six-lane divided (usually three lanes each direction); – 6: Freeway ramp (further indicated as diamond or cloverleaf ramp); – 7: At or near intersection; – 8: Other; – 9: Eight-lane divided; and – 9999: unknown. • CurveType: Determined from aerial imagery (categorical). This variable indicates whether the curve is to the left or right from the driver’s perspective (inside or outside of curve) during a particular time interval. Direction was confirmed by the forward video. CurveType was designated using the following conventions: – 0: No curve; – 1: Curve right; and – 2: Curve left. • PvmMarking: Determined from the forward video (categor- ical). This variable is a subjective assessment of the visibility of pavement markings. A driver’s ability to lane keep depends to some extent on having positive guidance as to the location of the traveled lane. The team reviewed the forward video and assigned pavement marking condition value according to the variable’s categories. It should be noted that pavement markings for the same stretch of roadway would appear dif- ferently at night or under wet conditions than during the day or dry conditions. Examples are shown in Figures A.5 and A.6. This variable was an attempt to determine the mark- ing visibility from the perspective of the driver and was defined with the following categories: – 0: Highly visible; – 1: Visible; – 2: Partially obscured; – 3: Obscured; and – 4: Nonexistent.• CurveSign: Determined from the forward video (categor- ical). This variable indicates whether some type of curve signing can be seen in the time intervals corresponding to a particular curve. Curve signing includes chevrons, curve warning signs, and curve advisory speed signs. A sign was indicated as being a curve warning when it simply provided additional information about the curve similar to those

115Source: UMTRI. Figure A.5. Pavement markings indicated as “highly visible” under nighttime conditions.Source: UMTRI. Figure A.6. Pavement markings indicated as “visible” under nighttime conditions.shown in Figure A.7. A sign with an advisory speed was also indicated as a curve advisory sign.Source: FHWA 2007. Figure A.7. Common curve warning signs.• RoadwayLength: In meters. Determined from the aerial imagery. This variable measures the length of each vehicle trace using a distance measuring tool in ArcMap. Roadway- Length is used in estimating density, crash rate, and drive- ways per mile. • ShoulderType: Determined from the forward video (cate- gorical). This variable classifies from visual observation the type of shoulder along a roadway section of a vehicle trace. Shoulder type is classified according to the following conventions: – 1: Paved; – 2: Paved/gravel; – 3: Gravel; – 4: Earth; – 5: Earth/paved; – 6: No shoulder; and – 7: Partially paved (includes 2 and 5 when used). • ShoulderWidth: In meters. Measured from the forward image by calibrating a known distance (lane width) in the image.• PavedShldrWidth: In meters. Measures the part of a shoul- der’s width that is paved. PavedShldrWidth is measured from the forward image by calibrating a known distance (lane width) in the image. • Radius: In meters. Measures the radius of a curve using aerial images. • PostedSpeed and AdvisorySpeed: In miles per hour. Curve advisory speed limit and posted speed limit were included in some of the data set’s vehicle traces. When they were not included, they were obtained from the forward imagery when available. When posted speed limit was not included and could not be obtained from the forward imagery, it was obtained where possible from the crash data of a roadway segment. Posted speed limit was included as a variable in the Michigan crash data. In most cases there were multiple crashes along a roadway segment; all these crashes were confirmed to have consistently occurred in places with posted speed limits. • DwyDensity: In driveways/m. Measured from aerial imagery and verified with the forward video when neces- sary. This variable counts the number of driveways along a vehicle trace. Driveway density is the number of driveways

116to the right of the vehicle in the direction of travel divided by vehicle trace length. Driveway density was calculated as indicated above but not included as a variable in the analysis. In retrospect, if driveway density were included, it would be more appro- priate to estimate it for a set distance in the immediate vicinity of the respective data points. Environmental Variables The following describes environmental variables that were either available with the UMTRI data set or were extracted. • Wiper: Provided with the data set (categorical). This vari- able indicates wiper blade status, which is an indicator of ambient precipitation in a time interval. Wiper status was designated using the following conventions: – 0: Off; – 1: Low; – 2: High; – 3: Invalid; and – 4: Intermittent. • Headlamp: Provided with the data set (categorical). This variable indicates headlamp status, which is an indicator of ambient lighting conditions in a time interval. Headlamp status was designated using the following conventions: – 0: Off; – 1: Parking; – 2: Low; and – 3: High. • SolarZenithAngle: In degrees. Provided with the data set. SolarZenithAngle can be used to determine time of day. • RoadSurf: Determined from the forward video (categorical). This variable specifies pavement surface condition accord- ing to the following conventions: – 0: Bare (no evidence of precipitation); – 1: Wet; – 2: Snow cover along edge of roadway but travel lane is bare or mostly bare; – 3: Snow cover along edges and within roadway but bare vehicle tracks; – 4: Light snow cover over entire roadway surface; and – 5: Medium or greater snow cover over entire traveled way. • TimeOfDay: In most cases, determined from the time stamp and forward video. This variable indicates the period when a vehicle trace occurred (categorical). It was recorded accord- ing to the following conventions: 0: Daytime; 1: Dawn/dusk; and 2: Nighttime.• EnvCondition: Obtained from the forward video. This variable indicates the prevailing atmospheric conditions when the driving trace occurred. Windshield wiper state can also be used to determine precipitation. EnvCondition indicates atmospheric conditions and may not correlate to pavement surface conditions. For instance, the prevailing environmental condition may be clear but there may be snow on the roadway surface. Environmental condition was designated using the following conventions: 0: Clear (no precipitation); 1: Light to moderate rain; 2: Heavy rain; 3: Light to moderate snow; 4: Heavy snow; and 5: Fog. • Lighting: Determined from the forward imagery. This vari- able indicates the presence of street lighting (categorical). Most nonintersection, noninterchange sections of rural roadways are unlit. Street lighting conditions were catego- rized according to the following conventions: 0: No overhead street lighting; 1: Continuous lighting along roadway segment; and 2: Intersection or interchange lighting but no continuous lighting on segment. • SegmentLength: Segment length was measured from aerial imagery and reported in meters. It was used in calculating crash density, vehicle density, and so forth. Measure of Exposure Variables The following variables were used as measures of exposure. These were either available with the UMTRI data set or were extracted as described. • AADT: In vehicles per day (vpd). Annual average daily traffic for each roadway was provided with the UMTRI data set. • TimeDriving: In seconds. The amount of time that a driver had been driving before the start of the vehicle trace was determined from the vehicle trace time stamp. Drivers who have been on the road for a significant time may be more likely to become drowsy or inattentive. • OnVehDensity: In vehicles per meter (v/m). The number of oncoming vehicles that passed the subject vehicle during the driving trace was determined from the forward video. Oncoming traffic density was calculated by dividing the total number of oncoming vehicles by segment length. • PassDensity: In v/m. Determined from the forward video, this variable provides the number of vehicles the subject vehicle passes. Passed traffic density was calculated by dividing total number of vehicles passed by the segment length.

117• OtherPassDensity: The number of vehicles traveling in the same direction that passed the subject vehicle was deter- mined from the forward video. The density of vehicles passing the subject vehicle (v/m) was calculated by divid- ing the number of passing vehicles by the segment length. • Following: Determined from the forward video. This vari- able indicates whether the subject vehicle was following another vehicle (categorical). A vehicle following very closely could also be detected by the forward radar. A vehicle is considered to be following another vehicle if it is close enough that the lead vehicle could influence its behavior. Figure A.8 shows an example of this. Figure A.9 shows an example of a situation in which a vehicle would not be con- sidered as following another. Following was designated by the following conventions: 0: Not following; 1: Following; and 2: Following closely.Figure A.8. Subject vehicle considered to be following lead vehicle.Figure A.9. Subject vehicle not considered to be following lead vehicle.Other Exposure Variables Other information available about the UMTRI data may also be used to determine exposure. It was reported that 80% of vehicle trips in the UMTRI FOT data were during the day and 20% were at night (LeBlanc et al., 2006). This information can be used to determine nighttime exposure. Trip length, travel by location (rural versus urban), and average trip distance by age and gender are available in the report by LeBlanc et al. (2006). • LDCrashes: The number of lane departure crashes that had occurred along the roadway where the vehicle trace was located was also determined. Crash data were available from the Michigan DOT as described in Chapter 3. The Michigan crash data contains four sequences of events forup to three vehicles. Lane departure crashes were identified by reviewing sequence of events and crash type. Data were available for 2000 to 2006 (7 years of crash data). If any of the following were indicated for any vehicle in a crash, the crash was identified as being a lane departure crash: – Crossed centerline or median. – Ran-off-road left. – Ran-off-road right. – Re-entered road. – Collision with fixed object:  Bridge, pier, or abutment;  Bridge parapet end;  Bridge rail;  Guardrail face;  Guardrail end;  Median barrier;  Traffic sign post;  Traffic signal post;  Luminaire support;  Utility pole;  Other pole;  Culvert;  Curb;  Ditch;  Embankment;  Fence;  Mailbox;  Tree;  Railroad crossing signal;  Building;  Traffic island;  Fire hydrant;  Impact attenuator; and  Other fixed object. Crashes that were identified as being lane departure crashes were extracted into a separate database and were plotted along with vehicle traces in ArcMap. Crashes falling along the vehicle trace were selected. The crash information was reviewed and any crashes which were not indicated as occurring on the roadway where the vehicle trace was located were discarded. • CrashDensity: Crash density in crashes per mile was cal- culated by dividing total number of lane departure crashes along the vehicle trace by the length of the trace. Identifying and Extracting Lane Departure Incidents One of the research questions addressed by the team is how to define lane departure crash surrogate events and to develop thresholds between those events on the basis of vehicle kinematics, such as lateral acceleration. In order to answer

118the two research questions, it was necessary to identify actual lane departures within the UMTRI data set so that this infor- mation could be used to begin identifying thresholds. This section describes how vehicle lane departure events were identified and extracted from the UMTRI data set. Discussion of thresholds is provided in Chapter 5. As indicated in the section on data preparation at the begin- ning of this appendix, some of the vehicle traces provided by UMTRI had been flagged as a lane departure or curve warning alert. Alerts were identified according to the road departure crash warning (RDCW) system field operational testing protocol. The thresholds set for the RDCW system alerts are discussed in Chapter 3. Their identification of alerts was used as a starting to point to identify lane departures. Other instances of lane departures were also found in the vehicle traces as described in the following sections. Identifying Lane Departure Incidents The main method to identify lane departures was to evaluate vehicle wheel path. Lane departures were also confirmed by a review of the forward imagery. Wheel paths were determined by calculating a vehicle position within its lane for each record of data (one record per 0.1 s of vehicle activity). The UMTRI data set had the following variables that were used to calculate wheel path. • TrackWidth: In meters. Width of vehicle wheelbase was used to calculate offset from the left and right lane lines. Since all vehicles in the data set were of the same type, track width was consistent between vehicles. • LaneWidth: In meters. Provided with the data set, this vari- able recorded the lane width for each time interval and was calculated within the instrumentation package based on pres- ence of left and right lane lines. Since lane width is calculated, it will vary from time interval to time interval even though in reality the lane width would not vary in this manner.• Offset: In meters. Provided with the data set, this variable indicates the vehicle offset from the center of the lane as calculated by the lane departure warning system. Offset is shown as the variable O in Figure A.10.Figure A.10. Schematic of variables used to calculate lane edge and wheel path locations.– Right and left lane edge and right and left wheel paths were calculated for each time interval for each vehicle path. Figure A.10 shows a schematic of the variables used to calculate lane edge and wheel path. – Lane line and wheel path locations are referenced from the right lane edge (RLE) which is set as the reference point (0). Position is positive moving to the left as shown in Figure A.11. Left lane edge is calculated using Equation A.4.Figure A.11. Lane edge and wheel path plotted by time interval.where LLEk = position of left lane edge for time interval k, RLEk = position of right lane edge for time interval k, and Wk = lane width measured at time interval k. Since RLE is always referenced as 0, LLEk = Wk. LLE RLE Ak k k= +W ( . )4

119Right wheel path is calculated using lane width, lane off- set, and track width according to Equation A.5: where RWPk = right wheel path (in meters) is the location of the right wheel path relative to the right and left lane lines for time interval k, Wk = lane width (in m) measured by RCWS for time interval k, T = vehicle track width, given as 1.73 m, and Ok = vehicle offset (in meters) is the distance between the centerline of the vehicle and the centerline of the lane for time interval k. Left wheel path was calculated using Equation A.6: where RWPk = right wheel path (in meters) for time interval k and T = vehicle track width, given as 1.73 m. Once wheel paths and lane edge were calculated, they were converted to feet since it was more intuitive to view wheel path traces in familiar units. A plot of lane edge and wheel path position was created in Excel for each vehicle trace as shown in Figure A.12. Each plot was evaluated to determine where lane departures occurred. LWP RWP Ak k= +T ( . )6 RWP Ak k k = − −W T O 2 5( . )Figure A.12. Vehicle wheel path intruding on left lane edge (left image) or right lane edge (right image).A lane departure was defined as a vehicle wheel path crossing over the right or left lane line and encroaching upon eitherthe shoulder or adjacent lane as shown in Figure A.13. Lane encroachment to the right was determined when the right wheel path (RWPk) had a negative value since the right lane edge was defined as 0. An encroachment to the left was deter- mined when the value for the left wheel path (LWPk) was greater than the lane width (Wk). Because there is some uncertainty in estimation of where the lane edges are, UMTRI used a buffer and only included encroachments that were greater than 0.1 m past the lane edge (LeBlanc et al., 2006). The research team adopted its convention and only included lane departures when the vehicle was more than 0.1 m (0.328 ft or 3.94 in.) beyond the left or right lane edge.Each wheel path plot was also inspected in conjunction with the corresponding forward imagery. In some cases, a lane departure had occurred but was intentional, such as a vehicle turning into a driveway or moving over for a parked vehicle. Figure A.13, for instance, shows a subject vehicle moving over for a stopped vehicle. Situations where a lane departure was intentional were not included as lane departures in the analyses. Additional Information Extracted for Lane Departures Once a lane departure was identified, additional information about the lane departure was extracted using the various data sets. The angle of departure (θ) from the roadway was calculated as shown in Figures A.14 and A.15. The approxi- mate linear path of the right wheel for a right-lane departure or left wheel for a left-lane departure was determined using vehicle path data just prior to the lane departure. The approx- imate linear path the departing tire would have followed had the vehicle not recovered was determined by estimation. The linear paths and geometrical relationships were used to deter- mine the angle of departure as shown in Figure A.15.

120(a) (b) Figure A.13. Identification of intentional lane departure for vehicle parked on shoulder: (a) vehicle wheel path shows lane departure and (b) video indicates lane departure was the result of the subject vehicle moving over for parked vehicle.Figure A.14. Estimation of wheel path for vehicle trace.Figure A.15. Schematic for angle of departure.

121The angle of departure was calculated using Equation A.7: where Angle of departure (θ) = angle that the vehicle departed from its original straight-line wheel path (in degrees), L = longitudinal distance vehicle traveled from the point the wheel departed from the straight-line Angle of departure Off θ( ) = ⎛⎝⎜ ⎞ ⎠⎟arctan ( L tot A. )7path to the point of maximum offset (Offmax), and Offtot = total distance from the straight- line path to the point of maxi- mum offset (Offmax). Maximum offset (Offmax) was the maximum distance that the wheel encroached beyond the edge of the lane. Maximum offset for right-lane departures was calculated by subtracting the offset value for the maximum point of encroachment to the right from the right-lane edge position. Maximum offset for left-lane departures was calculated by subtracting left-lane edge from offset at the maximum point of encroachment.