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83 C H A P T E R 5 Crash modeling is a relatively crude tool for determining the effects of individual roadway or roadside design factors. Vehicle dynamics simulation provides a much more direct and experimentally controlled method to examine these effects. Therefore, a vehicle dynamics simulation study was conducted as part of the research. 5.1 Introduction For at least four decades, vehicle dynamics software pack- ages such as Vehicle Dynamics Analysis Non Linear (VDANL) and CarSim (34, 35) have been used to aid in vehicle perfor- mance analysis, stability analysis, and accident reconstruction. Although some of the earliest vehicle simulation software were programs to aid in highway design (36â39), the use of multi-body vehicle simulation to study roadway design changes remains relatively rare. Many simulations have been compared with experimental data during the past few decades (40â50), and are being continually validated and updated. This study investigated the safety of highway medians by simulating median encroachments for several different vehicle classes, initial speeds, and encroachment angles. Both bumper height and vehicle positions during the simulation were considered as a means of analyzing roadway safety design factors such as location and height of cable barriers to be installed for that particular median. Furthermore, this study analyzes the impact of a driverâs input on the result- ing crash scenario. Unlike previous studies where these vary- ing steering and braking inputs were usually disregarded or grossly simplified, this study incorporates several steerâbrake combinations, and reveals the influence of these effects to be significant. For the present study, a relatively new software package called CarSim (developed by Mechanical Simulation) is used for the simulations. It was selected because it is the most widely used vehicle dynamics software in the industry, and it is easy to interface with external MATLAB and Simulink scripts. CarSim also has an advanced graphic user interface (GUI) allowing the user to build customized roadway profiles easily, select specific vehicles, and control the driverâs steering, accelerator, and braking inputs (35). The remainder of this chapter discusses details of a spe- cific study using vehicle dynamics simulations to examine the safety of rural divided highway medians. 5.2 Brief History of Vehicle Dynamics Simulations In recent years, vehicle dynamics simulations have been used for highway design and safety analysis purposes. In 1997, the software packages VDANL and Vehicle Dynam- ics Models for Roadway Analysis and Design (VDM RoAD) were used to predict the dynamics of a 1994 Ford Taurus (46). Results from this study showed a very realistic trend, both in the linear and non-linear range of the vehicle response, when compared to experimental data. Similarly, a program called PC-CRASH was used to reconstruct rollover crashes (49). When compared to real-life crash test data, the model was again validated. Benekohal and Treitererâs 1998 study was one of the first to apply CarSim as the vehicle dynamics software package for highway design analysis (51). In their study, traffic patterns on the highway in both normal and stop-and-go driving scenarios were simulated. Speed, steering, position, and suspension out- puts from the simulation were all compared to real-life experi- mental data and, after a regression analysis, an R-squared value of 0.98 proved the validity of the simulations. Another recent study published by FHWA created an in- depth driver vehicle module (DVM) to predict the driverâs response in certain crash situations on the highway (52). This study combined the VDANL model with a computational driver model that attempted to simulate the driverâs cognitive Median Encroachment Simulation
84 processes during driving. Although VDANL was originally designed for passenger cars, light trucks, and multi-purpose vehicles, DVM has only been created for passenger cars and Class 8 tractor trailers. The need for further use and testing of such software is apparent. For example, additional vehicle types should be included in the model, as should driver steer- ing inputs. Further testing involving vehicle dynamics simulations was carried out by the Federal Highway Administration (FHWA)/ National Highway Traffic Safety Administration (NHTSA) National Crash Analysis Center (NCAC) in 2008 (53). In this study, vehicle dynamics simulations with the Human- Vehicle-Environment (HVE) software package were com- pared with physical testing of a large passenger, pickup truck, and small passenger vehicle. Using cable barriers designed in accordance with the guidelines established in the NCHRP Report 350 study (54), this investigation examined the occur- rence of barrier underrides seen in real-life crash report data. Simulation results were strikingly similar to the data (from high-speed video footage and vehicle sensors) obtained in the physical testing. Although significant challenges remain related to the simulation of fine details of vehicle behavior during deep soil traversal, this study goes to further prove that the simulation of gross vehicle motion is accurate enough that off-road simulations are representative of phys- ical crash tests. 5.3 Methodology for Highway Median Safety Analysis The methodology used to analyze the safety of highway medians in the simulation portion of this study can be decomposed into the following six steps: 1. Define the roadway cross section, 2. Choose the vehicle, 3. Establish the simulationâs initial parameters, 4. Determine the driverâs inputs, 5. Run the simulation, and 6. Summarize the outputs, revert to Step 3, change the simu- lation parameters, and repeat. Each of these steps is outlined below in a specific example analyzing the influence of median cross-section design on vehicle trajectory during a median encroachment. 5.3.1 Step 1: Define the Roadway Cross Section To define the median cross section, both on- and off-road profiles and friction maps were created in CarSim. This study predominantly used an 18-m (60-ft) wide V-shaped median with a slope of 1V:6H, and a 2.4-m (8-ft) wide shoulder with a cross-slope of 4 percent as laid out in the Pennsylvania Depart- ment of Transportationâs design standards shown in Figure 5-1 (55). Additional medians of varying slope and width also were examined including: 12-m (40-ft) wide V-shape with 1V:6H slopes, 18-m (60-ft) wide V-shape with 1V:5H slopes, 18-m (60-ft) wide trapezoidal shape with 1V:5H slopes, and 18-m (60-ft) wide V-shape median with 1V:10H slopes. Further investigation of the importance of the median width was con- ducted. A 1V:6H V-shape profile was used with varying widths for this part of the study. 5.3.2 Step 2: Choose the Vehicle The next step in preparing the simulation was to specify the vehicle to be used. Using an external MATLAB script, nearly every parameter of the vehicleâfrom geometric con- figurations to inertial propertiesâcan be defined. This study uses vehicle parameters obtained by averaging data collected in the 1998 New Car Assessment Program (NCAP) (56). Although this survey is now a bit dated, in 2003, the NCHRP Roadside Safety Analysis Program (RSAP) Engineerâs Manual used vehicle distributions that matched closely to those in NCAP (57). Sprung mass, wheel base, track width, Center of Gravity (CG) location, and inertial properties were averaged for each vehicle class from NCAP, and Table 5-1 shows a sum- mary of these parameters (58). 5.3.3 Step 3: Establish the Simulationâs Initial Parameters To begin the simulation, the initial conditions must be specified. This study varied only the vehicleâs initial speed and departure angle upon encroachment, and all other vehi- cle states, including roll, pitch, and sideslip, were set to zero. Representative encroachment angles and vehicle speeds were obtained from the RSAP Engineerâs Manual (57). The angles varied from 2.5 to 32.5 degrees in 5-degree increments and speeds ranged from 8 to 88 km/h (5 to 55 mph) in 16 km/h (10 mph) increments, also including 115 km/h (70 mph). These speeds were chosen to represent the range of condi- tions under which an encroachment would occur. 5.3.4 Step 4: Determine the Driverâs Inputs A driverâs steering and braking inputs during a median encroachment are usually unknown, and therefore this study considered several generic but likely scenarios for driver intervention. Two scenarios represented active driver input: (1) steer the vehicle to the center of the median, and (2) attempt a return to roadway by steering to the edge of the pavement on the original travel lane shoulder. To imple-
85 ment these situations, the CarSim driver model was used with representative target point trajectories. A third steer- ing scenario, the âno steerâ condition in which the driver takes his/her hands completely off of the steering wheel, was also modeled. Figure 5-2 shows a top view of these targeted steering paths. Due to the specific encroachment angle and speed combi- nation, the driverâs attempt to recover to the shoulder edge, or even to the middle of the median, may not be physically possible. However, the steering inputs were defined in a way that simulates the driverâs attempt to direct the vehicle to a particular target point, whether or not the vehicle actually reaches that target point. In fact, in most of the simulations with high speeds and large encroachment angles, the tar- geted paths defined by the chosen steering input are dif- ferent from the actual trajectory of the vehicle during the encroachment due to the severe vehicle dynamics of these maneuvers. The braking was defined to be either a light braking (5 MPa of pressure at the cylinder) or hard braking (15 MPa) condition, Figure 5-1. 1V:6H V-shape median cross section. Vehicle class Sprung mass (kg) Wheel base (m) Track width (m) Front axle to CG CG height (m) Ixx (kg-m2) Iyy (kg-m2) Izz (kg-m2) Passenger, Small 969.0 2.524 1.446 1.021 0.519 392.60 1632.20 1798.80 Passenger, Large 1403.0 2.679 1.468 1.277 0.585 632.30 2749.70 2893.30 Pickup, Small 1409.4 2.948 1.424 1.396 0.620 571.25 3142.75 3326.25 Pickup, Large 1885.8 3.425 1.619 1.581 0.684 940.50 5344.00 5642.25 SUV, Small 1718.5 2.683 1.496 1.350 0.688 803.33 3367.00 3522.17 SUV, Large 2251.1 3.032 1.579 1.628 0.767 1157.25 5960.75 6111.00 Van 1847.5 2.947 1.589 1.480 0.698 992.33 4410.67 4617.83 Table 5-1. Vehicle parameters.
86 both with an anti-lock braking system (ABS) onboard. Each steering-braking combination was simulated for all possible vehicle-speed-angle runs tested, for a total of six driver actions simulated for each vehicle-speed-angle run. 5.3.5 Step 5: Run the Simulation To run the simulation, a MATLAB script was used to auto- mate the loading of vehicle parameters, initial conditions, median cross section, and the driver input scenarios. The vehicle was then simulated using a time step of 0.002 seconds, and the output variables were stored in a MATLAB struc- ture file for analysis and post processing. Each scenario was simulated for a total of 16 seconds, or up until the moment rollover was confirmed, whichever happened first. 5.3.6 Step 6: Summarize the Outputs and Repeat The simulation process was repeated over every possible vehicle, speed, encroachment angle, steering input, and brak- ing combination. This resulted in a total of 2,058 different simulations for each median profile, and the analysis of these results is provided in the next section of this report. 5.4 Data Post-Processing and Analysis Each simulated scenario generates one specific vehicle trajectory; however, some of these trajectories are far more likely to occur than others. To better represent the likelihood of each specific encroachment in real-life crash scenarios, a weighting method was used. Probabilities for the occurrence of each encroachment angle and speed were obtained from the RSAP Engineerâs Manual (57), thereby producing weight- ing factors for all possible speed and encroachment combina- tions. These are summarized in Table 5-2. Likewise, the probability of each vehicle class appearing on the highway was extracted from the 2001 National House- hold Travel Survey (59). It was assumed that the probability of accidents for each class is equal to the representation of each vehicle class on the road, which in turn is assumed equal to the class representation within the passenger vehicle fleet. The results of this study are summarized in Table 5-3. Although these statistics may seem a bit outdated, a more recent distribution produced in a 2006 study showed com- parable data. Passenger cars consisted of 54 percent of the roadway population while SUVs, vans, and pickup trucks collectively held 39.5 percent. Motorcycles, buses, and truck 0 10 20 30 40 50 60 70 80 90 100 -5 0 5 10 15 20 Longitudinal Distance (m) La te ra l D is ta nc e Fr om S ho ul de r E dg e (m ) Middle of Travel Lane Travel Lane Edge Shoulder Edge Median Swale Opposing Shoulder Edge Opposing Lane Edge Middle of Opposing Lane No Steer Median Recovery Road Recovery Vehicle's Initial Departure From Road Figure 5-2. Steering inputs used in simulations.
87 combinations accounted for the remaining vehicles on the road (60). Because there is no prior study that incorporates the prob- ability of the driverâs actions, the steering and braking inputs were weighted evenly across all runs. The total weighting factor used for each individual simu- lation is then a product of the individual weighting factors for each parameter used in the simulation. For example, for a crash scenario involving a large passenger vehicle (50.1 percent of vehicles on the road) departing the roadway at an angle of 12.5 degrees and a speed of 56 km/h (35 mph) (representing 5.13 percent of departures), the total weighting factor would be: 0.501 Ã 0.0513 = 0.0257. This quantity shows that of all the crash scenarios on the highway, this specific one occurs 2.57 percent of the time. After incorporating the weighting factors into the simula- tion data to better represent the probability of each specific crash scenario (vehicle, speed, departure angle, and driver actions combined), several contributing factors were ana- lyzed to determine their influence on accident causation. The following sections present the analysis of these factors, including median geometry, bumper height during the off- road trajectory, and driver intervention during the incident. 5.5 Influence of Median Geometry In an attempt to determine the influence of median cross- section design on the vehicle response during a median encroachment, simulations were run with varying median shape, slope, and width. All 2,058 possible combinations of inputs (vehicle, speed, angle, steering, and braking) were tested for each median. For the initial test of the median cross section, the five medians in question were as follows: 1. 1V:6H, 18-m (60-ft) wide, V-shape, 2. 1V:6H, 12-m (40-ft) wide, V-shape, 3. 1V:5H, 18-m (60-ft) wide, V-shape, 4. 1V:5H, 18-m (60-ft) wide, trapezoidal shape, and 5. 1V:10H, 18-m (60 ft) wide, V-shape. A key concern with median design is the increasing num- ber of SUV rollovers seen in median encroachment events. One downfall to using vehicle dynamics simulation programs to model these rollover situations is that currently there are no commercial software packages that correctly predict deep soil tire forces and hence soil-tripped rollover. However, this condition can be inferred by experimental criteria and post- processing of the vehicle trajectory. Criteria for soil-tripped rollover were found in a 2004 SAE experimental study wherein rollover is consistently seen when the vehicle exhibits a side- slip greater than 45 degrees at speeds greater than 32 km/h (20 mph) (60). After applying this designation for rollover to the simulation results for each vehicle class, the scenarios that did exhibit rollover during the off-road trajectory were recorded. Figure 5-3 displays the resulting distribution of rollover scenarios for all five medians listed above, filtered by vehicle class. As to be expected, and in agreement with existing crash statistics, the small SUV category experiences more than twice the number of rollovers as a small passenger vehicle. Figure 5-4 shows the same rollover scenarios as a function of the median cross-section. These results indicate that the width and shape of the median do influence rollover occur- rence. The narrow median (12 m or 40 ft wide) exhibited less rollover than the other medians, but this is most likely due to the smaller length of traversal and hence larger number of vehicles that enter the opposing lane, many of which rollover thereafter (which is not captured in these results). Because the median cross-section was shown to have a large effect on the vehicle response, specific aspects of the median were investigated. First, an 18-m (60-ft) wide, V-shape median with varying slope was considered. The evaluated slopes ranged from 1V:4H to 1V:10H, in increments of unit of median slope Initial speed (km/h) Encroachment angle (deg) 2.5 7.5 12.5 17.5 22.5 27.5 32.5 8 0.0002 0.0005 0.0005 0.0003 0.0002 0.0001 0.0002 24 0.0049 0.0119 0.0118 0.0088 0.0057 0.0034 0.0042 40 0.0151 0.0364 0.0359 0.0268 0.0174 0.0104 0.0127 56 0.0215 0.0519 0.0513 0.0382 0.0248 0.0149 0.0181 72 0.0205 0.0494 0.0488 0.0364 0.0236 0.0142 0.0173 88 0.0152 0.0367 0.0362 0.0270 0.0176 0.0105 0.0128 115 0.0200 0.0484 0.0478 0.0356 0.0231 0.0139 0.0169 Table 5-2. Speed and encroachment weighting factors. Vehicle Weighting factor Small passenger 0.089 Large passenger 0.501 Small pickup 0.090 Large pickup 0.101 Small SUV 0.063 Large SUV 0.063 Van 0.093 Table 5-3. Vehicle class weighting factors.
88 0 5 10 15 20 25 Pe rc en t o f A ll Ro llo ve r S ce na rio s (% ) 1V:6H 60 ft V 1V:6H 40 ft V 1V:6H 60 ft V Median Profile 1V:5H 60 ft Trap. 1V:10H 60 ft V Figure 5-4. Effect of median profile on vehicle rollover. Small Pass. Large Pass. Small Pickup Large Pickup Vehicle Class Small SUV Large SUV Van 0 2 4 6 8 10 12 14 16 18 20 Pe rc en t o f A ll Ro llo ve r S ce na rio s (% ) Figure 5-3. Rollover scenarios for all vehicle classes.
89 0 3 6 9 12 15 Pe rc en t o f A ll R ol lo v er S ce na rio s (% ) 1V:4H 1V:5H 1V:6H 1V:8H1V:7H 1V:9H 1V:10H Median Slope Figure 5-5. Effect of median slope on vehicle rollover. ratio (1V:4H, 1V:5H, etc.). Figure 5-5 shows the resulting roll- over scenarios in these simulations, sorted by the median upon which they were simulated. Figure 5-6 also shows the same rollover cases, sorted by the class of the simulated vehicle. In agreement with what was shown in Figure 5-3, the SUV and van population accounted for more rollovers than passenger vehicles and, generally speaking, the steeper sloped medians resulted in more rollover scenarios than did shallower slopes. These results give an initial impression that a less aggressive slope would lead to a safer median for all vehicles on the high- way, but upon further investigation, a more complex tradeoff between vehicle rollover and entry into the opposing lane is present. To help increase the understanding of this tradeoff, the location at which the vehicles came to a rest during the simu- lation was observed. Furthermore, the situations in which the vehicle rolled over were separated from those where the vehicle remained upright. The resulting data are displayed in Figures 5-7 and 5-8, respectively. Even though these data are useful, they still do not provide a clear understanding of the tradeoff under investigation. To provide more insight into this tradeoff, a ratio of those cases in which the vehicle entered the opposing lane to those which exhibited rollover, was created. Figure 5-9 shows this ratio for each simulated median slope, clearly displaying what was imbedded in the previous figures. It is now evident that a flatter median side slope will lead to a smaller number of rollovers, but at the cost of increasing the likelihood of an encroaching vehicle entering the opposing lane of traffic, and henceforth risking a head-on collision. To further investigate the impact of the median cross- section on vehicle response, all scenarios were run again for a 1V:6H, V-shaped median with varying width. The widths tested ranged from 12 to 23 m (40 to 76 ft), in increments of 1.8 m (6 ft). Figure 5-10 indicates that the widest median results in the highest number of rollovers and the narrow- est median the least. Although this may seem indicative that a narrower median is safer, in reality, the same tradeoff between vehicle rollover and entrance into the opposing lane is present here as well. Again, for the cases in which a vehicle did not exhibit roll- over, the location at the end of the simulation was recorded. Figure 5-11 shows the results from this portion of the experi- ment. From the figure, it can be seen that as the median width decreases, the number of vehicles entering the opposing lanes of traffic increases drastically. It is now evident that a narrower median does reduce the number of rollovers, but at the cost of the vehicle entering the
90 0 1 2 3 4 5 6 7 4:1 5:1 6:1 7:1 8:1 9:1 10:1 Opposing Travel Lane Back Slope Post-Swale Pre-Swale Downslope Original Travel Lane Original Shoulder Pe rc en t o f V eh ic le s to R ol lo ve r i n Ea ch A re a (% ) Figure 5-7. Vehicle locations at the onset of rollover for medians of varied slope. Figure 5-6. Rollover in medians of varied slope by vehicle class. 0 5 10 15 20 25 30 Pass Small Pass Large Pickup Small Pickup Large SUV Small SUV Large Van 1V:4H 1V:5H 1V:6H 1V:8H1V:7H 1V:9H 1V:10H Pe rc en t o f E ac h Ve hi cl e to R ol lo ve r o n G iv en S lo pe (% )
91 0 5 10 15 20 25 30 35 40 4:1 5:1 6:1 7:1 8:1 9:1 10:1 Pe rc en t o f V eh ic le s to C om e to a R es t i n Ea ch A re a Opposing Travel Lane Back Slope Post-Swale Pre-Swale Downslope Original Travel Lane Original Shoulder Figure 5-8. End locations for non-rollover simulation runs for medians of varied slope. Figure 5-9. Ratio of vehicles entering opposing lane to rollover for medians of varied slope. 0 0.5 1.0 1.5 R at io o f E nt er in g O pp os in g La ne to R ol lo ve r 1V:4H 1V:5H 1V:6H 1V:8H1V:7H 1V:9H 1V:10H Median Slope
92 12.19 14.02 15.85 17.68 19.51 21.24 23.16 0 3 6 9 12 15 Pe rc en t o f A ll Ro llo ve r S ce na rio s (% ) Median Width (m) Figure 5-10. Effect of median width on vehicle rollover. 0 5 10 15 20 25 30 35 40 45 12.19 m 14.02 m 15.85 m 17.68 m 19.51 m 21.24 m 23.16 m Pe rc en t o f V eh ic le s to E nd in E ac h Ar ea (% ) Opposing Travel Lane Back Slope Post-Swale Pre-Swale Downslope Original Travel Lane Original Shoulder Figure 5-11. End locations for non-rollover simulation runs for medians of varied width.
93 opposing lane, thus resulting in an increased probability of a head-on collision. Using the same ratio of incursion into the opposing lane to rollover at any time during the simulation as used in the median slope investigation, Figure 5-12 shows that a vehicle entering a 12-m (40-ft) wide median is almost twice as likely to enter the opposing lane as a vehicle on any other median width tested. These results again portray an obvious tradeoff between vehicle rollover and entrance into the opposing lane. 5.6 Bumper Height During the Off-Road Trajectory The position data from each simulation were recorded at the vehicleâs CG, and so the bumper position must be inferred. As a result, a market survey was conducted to estimate the average bumper heights for each vehicle class. Ground clear- ance data were obtained from vehicle manufacturersâ websites. Bumper clearance, measured to the bottom of the bumper of these surveyed vehicles, was determined by repeated measure- ments in a parking lot. After plotting the measured bumper clearance versus provided ground clearance, a linear trend between the two emerged. From this trend, the average bumper clearances for each vehicle class were inferred from the average ground clear- ances calculated from the manufacturerâs data. From these bumper clearances, the average distance between the bumper and the vehicleâs CG was easily calculated. This distance was then subtracted from the position data (output at the CG), resulting in the position of the bottom of the bumper through- out the entire simulation. Figure 5-13 shows the resulting cor- relation between the two sets of data, and these results agree with similar surveys (61). Hereafter, manufacturer-reported bumper clearance was used to infer bumper height for all simulation trajectories. As the term âbumper heightâ is commonly accepted in practice to be the distance between the ground and top of the bumper, the height of the bumpers themselves also was measured and then averaged. This quantity added to the cal- culated position of the bottom of the bumper to produce a value for the bumper height (e.g., top of the bumper) during the simulation. In Figure 5-14, the weighted distribution of bumper heights is shown after the previously defined weighting factors were applied. The first mode of data corresponds to the popula- tion of passenger cars and vans, whereas the second mode 12.19 14.02 15.85 17.68 19.51 21.24 23.16 0 0.5 1.0 1.5 2.0 Median Width (m) R at io o f E nt er in g O pp os in g La ne to R ol lo ve r Figure 5-12. Effect of median width on vehicle response.
94 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Ground Clearance (m) B um pe r C le ar an ce (m ) Cars and Vans SUVs and Trucks Figure 5-13. Inferring initial bumper height. 0.17 0.19 0.21 0.23 0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.40 0.42 0.44 0.46 0 5 10 15 20 25 30 Vertical Bumper Clearance Measured From Ground (m) A m ou nt o f A ll Ve hi cl es (% ) Figure 5-14. Initial bumper clearance distribution.
95 is representative of the SUV and truck population. There is clearly a disparity of about 20.5 cm (8 in.) between the two modes reflecting a great deal of incompatibility among bumpers on the highway today. Using results from all simulations, weighted distributions of bumper heights were generated for the following condi- tions: when the vehicle was at the shoulder edge, when at the median swale, and at several intermediate points. Figure 5-15 shows these resulting distributions overlaying a cross-section of the median type used in the analysis. For this particular median, the original travel lane is laterally defined at â4.2 m (â13.8 ft), the shoulder edge is at 0 m, and the median swale is at 7.344 m (24.079 ft). As can be seen in the figure, the initial bimodal distribu- tion disappears to have a single mode shortly after the vehicle departs the shoulder surface, and then it reappears before the vehicle reaches the swale point. Bumper traces representa- tive of a small SUV and small passenger vehicle are shown on top of the distributions as a means of investigating how these distributions are changing as the vehicle traverses the median. To isolate the effect of vehicle class, these two runs have the same initial conditions and driver inputs. After the SUV enters the median, it impacts the front slope, compress- ing the suspension and lowering its bumper to a height much closer to that of the passenger vehicle. As seen in the distri- butions, some vehicles impacted the ground surface, result- ing in a slight ground penetration with the front edge of the bumper. Figure 5-16 shows an image of the animation of this phenomenon. -4 -2 0 2 4 6 8 10 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 Lateral Distance From Shoulder Edge (m) Ve rt ic al H ei gh t M ea su re d Fr om G ro un d (m ) Bumpers Are Penetrating Ground Vehicles Are Airborne Small Passenger Bumper Trace Small SUV Bumper Trace Figure 5-15. Bumper height distributions at various lateral offsets from shoulder edge. Figure 5-16. Bumper ground penetration.
96 As the vehicles continued down the slope, the two modes appeared to separate again. At the swale point, most vehicles impacted the back slope at roughly the same height but major differences between vehicles emerged thereafter. For exam- ple, the passenger vehicle in Figure 5-15 is seen to bounce off of the ground before coming to rest on the upslope of the median, whereas the SUV becomes airborne and will most likely rollover after departure from the median area. Roll- overs and crashes during and beyond entry into the oppos- ing lane were not examined due to the obvious increase in contributory factors. Even so, these bumper location profiles are clearly useful in the design of median barriers as a func- tion of offset distance from shoulder. 5.7 Influence of Driver Intervention To illustrate the importance of steering input, the same vehicle, speed, encroachment angle, and braking was simu- lated three times on an 18-m (60-ft) wide, 1V:6H, V-shaped median. Each time, a different steering input was imple- mented. Figure 5-17 shows the vast differences in the vehicle response between these three scenarios. The white vehicle simulates the road recovery input, red is the median recovery, and the yellow vehicle has the no-steer condition as previ- ously discussed (see web PDF for color image). As can be seen here, only one of the three steering inputs led to rollover even though the simulations were otherwise identical. Looking at Figures 5-18 through 5-21, four differ- ent vehicle states (position, yaw, roll, and sideslip) are plotted for each of these three simulations. Again, the results are dras- tically different with only a variable factor being the steering input. To further illustrate the effects of steering input, the end locations of the vehicles were examined. Figure 5-22 shows the resulting data, and once again, vast disparities between simulations of different steering input are seen. As expected, clusters of data along each departure angle and speed are vis- ible, especially in the âno steeringâ case. As the steering input is altered, these clusters become more erratic and dispersed. If rollover events are organized by steering input, the resulting distribution is seen in Figure 5-23. As expected, aggressive road recovery steering leads to the highest amount of rollovers, while the passive âno steerâ condition results in the fewest. These findings indicate that the driverâs input is a primary contributing factor to rollover initiation and cannot be ignored in consideration of median geometric design. 5.8 Implications of Simulation Results for Median Design As presented in this section, there is one main safety trade- off in the design of earth-divided, traversable medians with- out longitudinal barrier. That is, the highway engineer must choose between designing a median to prevent vehicular roll- over or to design it with the intention of preventing against vehicles from encroaching upon the opposing lane of traf- fic. In medians with a longitudinal barrier, a major concern is where to place barriers in order to maximize the safety of vehicles departing the roadway. This section presents the results from this portion of the investigation and offers Figure 5-17. Influence of varied steering input.
97 0 20 40 60 80 100 120 -5 0 5 10 15 20 25 30 Longitudinal Position (m) La te ra l P os iti on (m ) Rollover Has Occurred Median Recovery Road Recovery No Steer Figure 5-18. XY position for varied steering input. 0 1 2 3 4 5 6 7 8 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Simulation Time (sec) Ve hi cl e Ya w A ng le (d eg ) Rollover Has Occurred Median Recovery Road Recovery No Steer Figure 5-19. Yaw angle for varied steering input.
98 0 1 2 3 4 5 6 7 8 -10 0 10 20 30 40 50 60 70 Simulation Time (sec) Ve hi cl e Ro ll An gl e (de g) Rollover Has Occurred Median Recovery Road Recovery No Steer Figure 5-20. Roll angle for varied steering input. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 Simulation Time (sec) Ve hi cl e Si de sl ip (d eg ) Rollover Has Occurred Median Recovery Road Recovery No Steer Figure 5-21. Sideslip for varied steering input.
99 0 20 40 60 80 100 120 140 160 180 200 -5 0 5 10 15 20 Longitudinal Distance (m) La te ra l D is ta nc e (m ) Median Recovery Roadway Recovery No Steer Figure 5-22. Final vehicle position. Roadway Recovery Median Recovery Steering Input No Steer 0 10 20 30 40 50 60 70 A m ou nt o f R ol lo ve r S ce na rio s (% ) Figure 5-23. Effect of steering input on vehicle rollover.
100 guidance for the design of median cross sections on divided highways. From the simulation data, general trends depicted the rela- tionship between a design parameter (median shape, width, etc.) and the frequency of both rollovers and cross-median crashes. For instance, when all other design variables are held constant, as the median width is increased, the frequency of rollover increased (see Figure 5-10). Table 5-4 shows the resulting effect of an increase in each parameter. In Table 5-4, an increase in slope means a steeper slope. From the simulation data, a trapezoidal median profile generally led to different outcomes than a typical V-ditch median profile. As seen in Table 5-4, the trapezoidal median decreased both the frequency of rollover incidents as well as the frequency of cross-median crashes. The vehicles in these simulations either steered back into the original travel lane safely or they were safely contained within the median. From these results, it can be concluded that a trapezoidal median cross-section will ultimately be safer than a V-ditch profile in the event of an off-road incursion. Additionally, when examining the vehicleâs roll angle and yaw rate for the two median shapes, the values for a trap- ezoidal median are much lower. This difference in the vehicle states ultimately shows that not only does a trapezoidal ditch lead to a safer end result of the incursion (rollover, cross- over, etc.), it also results in a much less aggressive and violent incursion for the vehicle as well. Even though the driverâs intervention is not technically a design parameter, as shown in the previous section, the driverâs actions must be taken into consideration. When the driver attempts to steer the vehicle after encroaching into the median, the propensity for vehicle roll increases. On the converse, if the driver does not give the vehicle any steer- ing input, the vehicle is more likely to cross over the median and enter the opposing lane of traffic if there is insufficient median width. As these driver inputs are typically unknown factors, it is extremely difficult to anticipate them. However, when considering the installation location of median barrier, the driver will most likely react in an effort to avoid impacting the barrier. In this manner, the anticipated driver intervention must be considered as an additional design parameter. The data presented in this study implemented three generic steer- ing conditions, and did not account for the effect of a median barrier on the driverâs perception. Even with these generalities in design parameters, there still are no clear âoptimalâ median slope-width combinations. To help highlight these median combinations, the simulations that led to either a rollover or cross-median crash scenario were marked. The median slope and width were recorded for each of these simulations. Probabilities of rollover and cross-median scenarios occurring were then calculated for each slope-width combination. From here, it was determined if each of the median cross-section combinations was more likely to lead to rollover or cross-median crash. The results from this analysis were plotted on an XY scatter to show the resulting trends between the parameters in question. Fig- ure 5-24 shows the outcome of this analysis. As can be seen, there is a dividing line or boundary where any combinations of median width and slope below the line are most likely to lead to a cross-median crash and any com- bination of median width and slope above the line are most likely to lead to a rollover. Thus, Figure 5-24 provides guid- ance that can be used by highway engineers to determine the tradeoff between median design parameters as a function of likelihood of cross-median and rollover crashes. Another design characteristic of the median is where to install a median barrier to help maximize safety for all travel- ers on the highway. Figure 5-15 shows the clearance height of the vehicleâs bumper during a median encroachment, but the top of the bumper (typically referred to as the âbumper heightâ) must be considered as well as the bottom. Using averages (per vehicle class) for the thickness of the bumper itself, the bumper height was calculated from the already cal- culated bumper clearance data. The two modes, representing the passenger and SUV vehicle populations respectively, were recorded at various offsets from the shoulder edge. The bum- per position trace during a median encroachment was then created from this position by position mode data. The resulting traces of bumper top and bottom are shown in Figure 5-25. The most likely vertical position for the top and bottom of the bumper of all vehicles is represented with the four position traces shown in Figure 5-25. Figure 5-25 shows vehicle bumper clearance height dis- tributions for small passenger cars and small SUVs during Increase in Frequency of rollover Frequency of cross-median crashes Median width â â Median slope â â Median shape (trapezoid vs. V-ditch) â â Driverâs intervention â â Table 5-4. Effect of increase in each parameter on rollover and crossover crashes.
101 4H:1V 5H:1V 6H:1V 7H:1V 8H:1V 9H:1V 10H:1V 12.19 14.02 15.85 17.68 19.51 21.24 23.16 Median Slope M ed ia n W id th (m ) Rollover Cross-Over Cross-Over Prone Median Profiles Rollover Prone Median Profiles Figure 5-24. Optimal median geometry analysis. -4 -2 0 2 4 6 8 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Lateral Distance From Shoulder Edge (m) Ve rt ic al H ei gh t M ea su re d Fr om G ro un d (m ) SUV/Truck Passenger Road Profile Figure 5-25. Bumper height and clearance modes throughout the median incursion.
102 a median encroachment. The median cross-section simu- lated was 18 m (60 ft) wide with 1V:6H cross-slopes. The AASHTO Roadside Design Guide (2) and results from the survey in the present study indicate that barriers placed in medians with a similar cross-section to that which was simu- lated are typically placed near the edge of the shoulder or near the swale point in the center of the median where the foreslope and backslope intersect. The vehicle dynamics sim- ulation results for the height of the vehicle bumper during a median encroachment, shown in Figure 5-25, indicate that at the outside edge of a 1.2-m (4-ft) paved shoulder (repre- sented by a zero offset in Figure 5-25), the mode (or most common value) for the clearance height of a small passenger car bumper is approximately 0.2 m (8 in.) above the ground. A small SUV has a mode value for bumper clearance height of approximately 0.32 m (12.5 in.). A typical small passenger car has a bumper height of 0.15 m (6.0 in.), while a small SUV has a typical bumper height of 0.22 m (8.7 in.). This sug- gests that bumper profiles of small passenger cars and small SUVs range from 0.20 to 0.36 m (8 to 14 in.), and 0.32 to 0.54 m (12.5 to 21.2 in.), respectively. The suggested mount- ing heights (2) of cable median barrier are 0.69 to 0.76 m (27 to 30 in.) to the top cable in a three-strand system. The bottom cable height is typically 0.51 to 0.61 m (20 to 24 in.) above the ground. For the strong post W-beam guardrail, the mounting height recommended is 0.69 m (27 in.) to the top of the rail element. The bottom of the rail element is typi- cally 0.43 m (17 in.) above the ground. The bumper height envelope from the vehicle dynamics simulations suggests that strong post W-beam will likely be impacted by the bumpers of some small SUVs within the mounting height range of the barrier when installed at the edge of the paved shoulder in accordance with AASHTO policy. This is not necessarily the case for small passenger cars, because the bumper height envelope is lower than strong post W-beam barrier profile. The same findings apply for three-strand cable median bar- riers, where the bumper height envelope for some small SUVs will impact the barrier within the range of mounting heights for the barrier, but the bumpers of small passenger cars will not necessarily impact a three-strand cable barrier within the typical range of mounting heights. The results in Figure 5-25 show that the mode value of the bumper clearance height trajectories remains relatively consistent as small passenger cars and SUVs traverse a 6H:1V foreslope during a median encroachment; however, a small proportion of vehicles were found to penetrate the ground before reaching the swale point. The AASHTO Roadside Design Guide (2) suggests that cable median barriers can effec- tively redirect vehicles on 1V:6H foreslopes if placement of the barrier in the area between 0.3 and 2.4 m (1 to 8 ft) offset from the swale is avoided. The vehicle dynamics simulation results in the present study indicate that ground penetrations occurred at approximately 2.0 m (7 ft) and approximately 3.5 m (12 ft) from the swale point, respectively. The latter value is larger than that suggested by AASHTO. The bumper clearance height trajectories approximately 0.3 m (1 ft) from the swale point on the foreslope are similar to those at the edge of the shoulder, and no ground penetrations were iden- tified in the simulations at this location. This suggests that median barrier mounting heights, when offset approximately 0.3 m (1 ft) from the swale point on 1V:6H foreslopes, may be effective in redirecting small passenger vehicles as the bumper clearance height remains relatively constant with respect to the ground for approximately 1.0 m (3 ft) after crossing the swale point, particularly if the barrier deflection is less than 1.2 m (4 ft). The same is not necessarily true for small SUVs because the bumper clearance heights (and the range of simu- lated bumper height values) immediately before and after the vehicle traverses the swale point change considerably over a short lateral distance. In summary, the vehicle dynamics simulation results in Fig- ure 5-25 show a broad range of simulated bumper heights for vehicles traversing a median, particularly after those vehicles have passed the swale and are traversing the upslope toward the opposing roadway. This has potential implications for bar- rier placement and barrier mounting height. The results in Figure 5-25 suggest small passenger car bumper traces remain relatively constant near the median swale, so that placement of a median barrier near the swale may be effective for this vehicle class. However, the range of bumper heights is larger for small SUVs after crossing the swale point, so the effectiveness for SUVs of barriers placed on the upslope is a potential concern. No simulations of barrier impacts have been performed in this research; such simulations, especially for barriers located on the upslope beyond the median swale, should be considered in NCHRP Project 22-22.
