May 2006

Foreword

This report summarizes work performed to model, evaluate and verify the safety benefits of an improved version of the Roll Advisor and Controller (RA& C) on-board safety system.

A U.S. Department of Transportation (USDOT) Intelligent Vehicle Initiative (IVI) Field Operational Test (FOT) led by Freightliner evaluated an RA& C on-board safety system. The RA& C system assists commercial vehicle drivers, especially drivers of tanker trucks, to avoid rollover crashes. The RA& C is comprised of two components that perform two distinct functions: to inform drivers when they have performed a maneuver with a high risk of rollover (the roll stability advisor [RSA] component), and to initiate autonomous braking to prevent a rollover (the roll stability control [RSC] component).

All of the data analyzed in this report came from the Freightliner IVI FOT. Data were collected on six Freightliner tractors pulling tank trailers of liquid nitrogen in revenue service during late 2000 through 2001. The methods for estimating the benefits of a safety system were developed by Battelle as part of the independent evaluation of the FOT. This report describes how the methods of the independent evaluation were applied to the data of the FOT to predict the benefits of an improved RSC, without conducting a new field test of the system.

Although the report can be helpful to the general public in understanding an on-board safety system, the report is primarily targeted towards commercial motor carriers and their drivers.

This publication is considered a final report and does not supersede another publication.

Notice

This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use thereof.

This report does not constitute a standard, specification, or regulation.

The United States Government does not endorse products or manufacturers. Trade or manufacturers' names appear herein only because they are considered essential to the objective of this document.

Technical Report Documentation Page (Form 1700.7)

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Table of Contents

Executive Summary. ii

1.0...... Introduction. 1

2.0...... Background. 1

3.0...... Approach. 2

4.0...... Simulation. 3

4.1 Basic Vehicle Model 3

4.2 Roll Stability Control Model 5

4.3 Model Validation. 5

4.4 Simulation Example. 6

5.0...... Benefits Assessment 10

5.1 Probability Estimates. 10

5.2 Benefits Formula. 12

5.3 Number of Rollovers Prevented. 13

5.4 Effect of Circumstances on Performance. 14

6.0...... References. 16

Appendix A.. 17

Appendix B.. 26

Appendix C.. 31

List of Figures

Figure 1. Path of the Truck in One of the Critical Conflicts. 7

Figure 2. Speed through the Path of Figure 1, as in the FOT and Increased Nearly to the Point of Rollover 7

Figure 3. Simulation of the RSC to Reduce Speed and Avoid a Rollover 8

Figure 4. RSC Limits the Lateral Acceleration of the Trailer 9

Figure 5. RSC Limits the Roll Angle of the Trailer 9

List of Tables

Table 1. Summary of Parameters in the VDANL Model for the Two Load Conditions. 4

Table 2. Fill Levels of Conflicts Identified in the FOT Data. 4

Table 3. Deceleration Achieved by the RSC in an Actual Vehicle on the Test Track and by the VDANL Model of the RSC in a Similar Situation. 6

Table 4. Crash Prevention Estimates. 14

Executive Summary

This report summarizes work performed to model, evaluate, and verify the safety benefits of an improved version of the Roll Advisor and Controller (RA& C) on-board safety system.

The RA& C on-board safety system includes two major components consisting of the Roll Stability Advisor (RSA) and the Roll Stability Control (RSC). The RSA component informs drivers when they have performed a maneuver with a high risk of rollover; the RSC component initiates autonomous braking to prevent a rollover due to excessive speed in a curve. The combined RA& C constantly monitors cornering forces while the vehicle is in operation. An on-board computer in the RA& C processes the information received from the on-board sensors to detect when there is risk of a rollover. If a high risk of rollover is detected, the RSC component initiates braking automatically to slow the vehicle without driver intervention.

The RA& C on-board safety system was originally tested in the U.S. Department of Transportation (USDOT) Intelligent Vehicle Initiative (IVI) Freightliner Field Operational Test (FOT). In the FOT, the RSC version that performed autonomous braking used only the engine retarder (often referred to as the Jake Brake), which uses engine compression to slow the vehicle.

From the independent evaluation of the FOT, it was found that the RSC could provide greater safety benefits by engaging the service brakes, which provide faster and more positive braking forces to potentially increase the effectiveness of the system to reduce rollover and road departure crashes. Therefore, the vendor who manufactured the RSC subsequently developed an improved system that used the service brakes to slow the vehicle in response to detected critical events.

In order to estimate the effectiveness of the improved RSC without conducting another FOT or extensive track testing, an alternative evaluation approach was necessary. The approach used a computer simulation tool to model the improved RSC to predict how the RSC would have behaved in situations (i.e., driving conflicts) similar to those observed in the Freightliner FOT.

Using the simulations, the RSC was estimated to prevent about 53 percent of the rollovers resulting from excessive speed in a curve. To estimate the combined effect of using both the RSA and RSC, it was assumed that the RSA would prevent some near-rollover situations from occurring due to driver education, and that the RSC would prevent some of those that remain from actually leading to a rollover. Therefore, the combined RA& C was estimated to prevent 69 percent of heavy vehicle rollovers that are caused by excessive speed in a turn.

1.0 Introduction

This report summarizes work performed to model, evaluate and verify the safety benefits of an improved version of the Roll Advisor and Controller (RA& C) on-board safety system.

A U.S. Department of Transportation (USDOT) Intelligent Vehicle Initiative (IVI) Field Operational Test (FOT) led by Freightliner evaluated an RA& C on-board safety system. The RA& C system assists commercial vehicle drivers, especially drivers of tanker trucks, to avoid rollover crashes. The RA& C is comprised of two components that perform distinct functions:

• The roll stability advisor (RSA) component – to inform drivers when they have performed a maneuver with a high risk of rollover.

• The roll stability control (RSC) component – to initiate autonomous braking to prevent a rollover.

All of the data analyzed in this report came from the Freightliner IVI FOT. Data were collected on six Freightliner tractors pulling tank trailers of liquid nitrogen during late 2000 through 2001. The methods for estimating the benefits of a safety system were developed by Battelle as part of the independent evaluation of the FOT. The methods are described in detail in the report on the independent evaluation [Battelle, 2003] and its appendices [Battelle, 2003a]. This report describes how the methods of the independent evaluation were applied to the data of the FOT to predict the benefits of an improved RSC, without conducting a new field test of the system.

On the basis of the analysis, about 53 percent of heavy vehicle rollover crashes caused by excessive speed in curves can be prevented by the Roll Stability Control. The analysis corroborated the manufacturer’s claim that the device can be quite useful in preventing rollover crashes, but it also confirmed the manufacturer’s caution that the device does not prevent all crashes.

2.0 Background

The RA& C includes two major components consisting of the Roll Stability Advisor (RSA) and the Roll Stability Control (RSC). RSA is a passive system that communicates with the driver about recent rollover conditions. The advisor system warns the driver after the event has occurred with the objective of changing driver performance in similar future driving situations. RSC is an active system that interacts with the vehicle to correct a current rollover situation. The RA& C constantly monitors cornering forces while the vehicle is in operation. An on-board computer in the RA& C processes the information received from the on-board sensors to detect when there is risk of a rollover. If a high risk of rollover is detected, the RSC component initiates braking automatically to slow the vehicle without driver intervention.

In the FOT, the RSC version that performed autonomous braking used only the engine retarder (often referred to as the Jake Brake). The engine retarder uses engine compression to slow the vehicle. Meritor WABCO, the RSC manufacturer involved in the FOT, recognized that greater safety benefits could be realized by engaging the service brakes. The service brakes provide faster and more positive braking forces to potentially increase the effectiveness of the system to reduce rollover and road departure crashes. Therefore, the vendor who manufactured the RSC subsequently developed an improved system that used the service brakes to slow the vehicle in response to detected critical events.

This RA& C Deployment Planning Project originally focused on the version of the RA& C that was tested in the Freightliner FOT. However, recognizing that the vendor did not intend to offer this early version as a commercial product, it became clear that any deployment plan for the RA& C system should focus on accelerating the availability and use of the improved RSC (i.e., the RSC that uses the service brakes).

In order to estimate the effectiveness of the improved RSC without conducting another FOT or extensive track testing, an alternative evaluation approach was necessary. The approach used a computer simulation tool to model the improved RSC and predict how the RSC would have acted in situations (i.e., driving conflicts) similar to those observed in the RA& C FOT.

The accuracy in simulating a physical system depends on understanding the dynamic operating characteristics of the system and mathematically representing those dynamic operating characteristics accurately in the computer model. The model was developed using a commercially available tool, Vehicle Dynamics Analysis, Non-Linear (VDANL). [1] This tool incorporates equations of motion that explicitly describe vehicle dynamics in the longitudinal, lateral, and vertical directions in addition to independent wheel spin modes. Section 4 describes the tool and model in greater detail.

As part of the project, the RSC vendor also performed track tests at the Transportation Research Center in East Liberty, OH to obtain input data needed to calibrate the VDANL model for the improved RA& C. These data included typical brake pressure and deceleration time histories.

3.0 Approach

In the independent evaluation of the FOT, vehicle simulations were used to provide an objective and quantitative calculation of crash probability. A similar approach was used to estimate the number of crashes that could be prevented by the improved RSC. Unique events from the FOT of a truck equipped with the improved RSC were simulated.

There were no rollovers in the FOT. However, the independent evaluation identified 137 “critical conflicts”. These were events that had dynamic characteristics that preceded a rollover crash. Specifically, the lateral acceleration measured during the event was a significant fraction of the estimated static rollover threshold of the vehicle at the time of the event. If each of these 137 events were to occur again many thousands of times, each occurrence would differ slightly. For example, the speed may be slightly higher, the load may be a little fuller, or the driving path may be slightly different. These differences can be considered to be perturbations of the actual event in the FOT. A small fraction of the combinations of these perturbations will result in a rollover crash. It is this fraction that must be calculated to assess the improved RSC’s ability to eliminate crashes.

In short outline form, the procedure is:

1. Simulate the conflict exactly as it was recorded in the FOT.

2. Simulate the conflict again with the speed 1 ft/s faster, but do not change other conditions.

3. Keep repeating Step 2 until the vehicle rolls over or can no longer maintain its path.

The result of these three steps is a measure of the severity of the conflict. These steps are carried out separately for each conflict. A statistical procedure then estimates the probability of a rollover crash if all the conflict scenarios were repeated, say, ten thousand times, each time with a small perturbation. This process is illustrated in greater detail under the heading, “Simulation Example” in Section 4.4.

The procedure was followed first using a simulation model of an ordinary truck—one without the RSC. The entire procedure was repeated with a simulation model of a truck equipped with the improved RSC. The reduction in probability of a rollover attributable to the RSC was calculated, and, from this, the expected number of rollovers prevented was calculated based on historical crash data [Battelle, 2003b].

4.0 Simulation

A commercially available computer model of a heavy vehicle was adapted to evaluate the improved RSC. The simulation focused on how a tractor pulling a cargo tank semitrailer, similar to the vehicles in the FOT, would behave if it were equipped with the improved RSC.

4.1 Basic Vehicle Model

As part of the independent evaluation, the FOT vehicles were modeled in Vehicle Dynamics Analysis, Non-Linear (VDANL) Version 6.0.[2] This tool has been in development since the 1980s. It has been applied by its developer in contracts for various administrations within the DOT, including light vehicle rollover work for National Highway Traffic Safety Administration (NHTSA), and in contracts for private companies. By selecting parameters to describe the vehicle, VDANL can be applied to vehicles from race cars to tractor-semitrailer combinations. This rigid-body model incorporates equations of motion that explicitly describe vehicle dynamics in the longitudinal, lateral, and vertical directions in addition to independent wheel spin modes. The sprung and unsprung mass motions are modeled separately in the pitch, roll, heave, and lateral modes. The longitudinal motions are for the total vehicle while the sprung and unsprung masses rotate together in yaw. The model also shows a two-axle trailer connected to the tractor through a compliant fifth wheel. The model integrates the nonlinear equations of motion, incorporating driver actions and external inputs. The VDANL model, including the equations of motion and the methods for measuring parameters, is documented in Allen et al. [1992].

The description of a vehicle in VDANL for the independent evaluation is defined by several parameters. When possible, actual measured values were used in the model. For example, the wheelbase and track widths (see Table 1) of the truck used in the track testing were measured. Axle loads were also measured during the track test. However, the height of the vehicle’s center of gravity and inertias had to be estimated. Other parameters such as roll stiffness, throttle and steering lags, and steering geometry were assumed to be typical of five-axle trucks.

Table 1. Summary of Parameters in the VDANL Model
for the Two Load Conditions

Vehicle weight and center of gravity are key parameters in determining the rollover thresholds of a heavy vehicle. The gross vehicle weight was not the same for all of the 137 conflict cases analyzed. The modeling accommodated this variability by establishing three groups according to Table 2. The mass of the modeled vehicle was always within about four tons of the mass of the FOT vehicle in the conflict being modeled. Appendix C contains a more complete description of the differences between the models of the full and partially loaded cases. The vehicle was not in danger of rolling over in the conflicts where the tank was empty or nearly empty, and those conflicts were not simulated in the present exercise. The primary differences in the parameters are in the vehicle sprung and unsprung mass weights, vehicle sprung mass center-of-gravity heights, and the vehicle inertias. Minor variation in some of the driver model feedback parameters was made between models to obtain good speed and curvature tracking.

Table 2. Fill Levels of Conflicts Identified in the FOT Data

VDANL incorporates a driver model with access to the gains of the closed loop system. These can be modified to achieve the appropriate velocity, steering, or curvature input response. During the FOT, vehicle speed and yaw rate of the tractor were measured. The ratio of the yaw rate to the speed is the curvature of the path being traversed by the truck. Hence, the vehicle speed and road curvature were used as inputs to the VDANL model.

4.2 Roll Stability Control Model

A model of the improved RSC safety system was incorporated in the VDANL model of the tractor-trailer combination. The basic vehicle model developed and validated in the independent evaluation was used as a starting point. The model was expanded to include the improved RSC that applies the service brakes.

The vehicle model simulates several levels of braking by the improved RSC depending on the vehicle weight and level of lateral acceleration during the maneuvers. The improved RSC provides for different levels of intervention according to the perceived severity of the situation. The lowest level calls for engine torque reduction, and the higher levels add the engine retarder or control pressure signals to apply the drive axle and trailer brakes.

Meritor WABCO provided Battelle with qualitative and quantitative descriptions of the brake pressures, vehicle decelerations, and time constants it had measured on an actual truck equipped with RSC. A description of the RSC was coded in the VDANL model by adjusting the braking torques and gear-shifting to provide braking characteristics similar to the Meritor WABCO system. The system must estimate the vehicle mass; the mass was assumed to be measured exactly in the simulation.

4.3 Model Validation

The original model and parameter set to describe the vehicle itself were validated through comparison with data from full-vehicle tests performed at the Transportation Research Center (TRC) in East Liberty, OH as part of the independent evaluation [Battelle, 2003a].

The VDANL models were exercised using inputs from several representative test track maneuvers and several representative FOT maneuvers. In addition, some of the FOT runs were simulated using the different gross vehicle weight models. The accuracy of the simulation results with the test track runs validated that the VDANL truck model responses are similar to an actual truck performing these maneuvers. Close agreement of the simulation and representative maneuvers from the FOT gave confidence that the simulation could be used for simulating the improved RSC for the 137 FOT conflict cases [Battelle, 2003, pages 5-25 to 5-35].

The ability of the RSC model to emulate the performance of the improved RSC product was demonstrated by simulating maneuvers that had been performed at TRC by Meritor WABCO. Quantitative and qualitative comparisons proved that the behavior of the RSC had been captured in the model. The actual truck used to validate the model of the vehicle in the independent evaluation was a nitrogen-style tanker filled with water; except for the load, it was nearly identical to those in the FOT. The vehicle used to validate the model of the RSC in the present effort was a flatbed loaded with blocks of concrete to provide a high center of gravity, which differed from the tanker used in previous experiments and described in the vehicle model. Its roll dynamics are somewhat different from those of a vehicle with a tank trailer; however, the RSC is contained entirely on the tractor, and its braking commands are similar for any fully loaded combination vehicle. The center column of Table 3 gives the peak deceleration recorded on the actual vehicle at TRC for cases of high and low rollover risk for a fully loaded vehicle and for a low rollover risk in a partially loaded vehicle. The right column gives the peak deceleration calculated in the model for similar maneuvers on fully and partially loaded vehicles.

Table 3. Deceleration Achieved by the RSC in an Actual Vehicle on the Test Track and by the VDANL Model of the RSC in a Similar Situation

4.4 Simulation Example

The 137 conflict cases identified in the FOT were used as the basis for a special simulation analysis to determine the efficacy of the RSC.[3] The table in Appendix A lists a summary of input and output information for each of the conflicts. The leftmost “input” columns in Appendix A give information that characterize the type of curve, vehicle information, and the initial speed of the maneuver. The columns to the right in the appendix present “output” results from the simulations such as the maximum lateral acceleration with and without the system, and the speed at which rollover occurs with and without the system. The introductory material to the appendix describes the columns more fully. There is one page for each conflict in Appendix B, where the maneuver path is displayed along with a time history of the speed lateral acceleration and other measurements.

For each conflict, vehicle speed was perturbed to induce a vehicle rollover. Starting with the speed profile recorded for the conflict, the speed was incremented by 1 ft/s (about 0.7 mph) for the entire maneuver, and the simulation was run. If no rollover was observed, the speed profile was incremented by an additional 1 ft/s and the simulation repeated. Increasing the speed in 1 ft/s increments, each conflict was perturbed until a vehicle rollover was observed.

The independent evaluation established the speed perturbations that could be tolerated by the vehicle in each of the conflict cases before it resulted in a rollover. With the introduction of the improved RSC, the exercise was repeated to determine if the dynamic envelope that separates the conflict case from a definite rollover could be widened (i.e., could the truck equipped with the RSC enter a curve at speed perturbations higher than an identical truck without the RSC and not roll over).

Figures 1 through 4 illustrate how this process was carried out for one of the 137 conflict events. This conflict was recorded on Truck 4 during trip 1072 at approximately the time marker of 622. (This conflict is highlighted in Appendix A, and shown in Appendix B.7.) The first figure is a “bird’s eye view” of the intended maneuver. The truck was coming from the upper left and turned right through two curves before driving off to the south. The black dot in Figure 1 indicates the point of interest—where the highest lateral acceleration was measured during the FOT. In Figure 2, the lower, lighter line is the speed history of the Praxair truck as it drove through the path in the FOT. It began around 17 mph, sped up gradually, slowed briefly again as it made the curve, and then accelerated out of the curve. In the first simulation of this maneuver, the simulated truck followed the path shown in Figure 1 at the speeds shown in the lower line of Figure 2—the same path and speed measured on the real truck in the FOT. The black dot on this trace at 18.2 mph indicates the speed at the moment where the peak lateral acceleration was observed. This is the reference speed for calculating the probability of a crash in Section 5.1

Figure 2. Speed through the Path of Figure 1, as in the FOT and Increased Nearly to the Point of Rollover

The simulation was then repeated with successively higher speed increments until the simulated truck rolled over. The upper, heavier trace in Figure 2 shows the speed of the truck when it was 4 mph faster than the original FOT speed. This was as fast as the truck could go through the path without rolling over. At the next speed increment, the simulated truck rolled over. That is the first piece of important information from the simulation: if everything were identical to the actual event observed in the FOT, except that the driver entered the maneuver 4.8 mph faster than the actual FOT speed, the truck (without the RSC) would have rolled over.

The model of the RSC was implemented for the next simulation of this maneuver. When the vehicle was about to roll over, the RSC called for the brakes to be applied, so an appropriate brake application was simulated. The truck slowed down and did not roll. Figure 3 shows how the RSC affects the speed of the simulated truck. The solid line is the speed of the truck without RSC, just below the rollover threshold. The dotted line indicates the speed of the truck equipped with RSC. Up to the point of intervention, the two trucks had the same speed. At the point indicated by the arrow, the brakes were applied, the simulated vehicle slowed down, and a rollover was avoided.

Figure 4 shows the lateral acceleration calculated at the trailer center of gravity during these simulations. As the acceleration reaches about 0.3 g, the RSC activates and reduces the rolling tendency of the trailer. The static rollover threshold of a filled FOT vehicle was measured to be about 0.37 g [Figure 4-6, Battelle, 2003]. At the next higher speed increment, the vehicle without the RSC would have reached a peak trailer lateral acceleration of 0.40 g (the value in Appendix A for this example case) and rolled over. When the vehicle with RSC was simulated at the next speed increment, the peak lateral acceleration was limited to 3.0 g, as noted in Appendix A.

Figure 5 compares the roll angles of the trailers on the unequipped and equipped vehicles. The plot with the wide swings in roll angle is on the truck without RSC. The roll angle reaches about 15 degrees, and our earlier work on the test track showed that this is well beyond the point of safe maneuvering. The roll angle of the trailer on the vehicle with RSC is limited to a much safer 5 degrees.

Figure 3. Simulation of the RSC to Reduce Speed and Avoid a Rollover

Figure 4. RSC Limits the Lateral Acceleration of the Trailer

Figure 5. RSC Limits the Roll Angle of the Trailer

Finally, the simulated truck was launched into this same path at successively higher starting speeds until eventually the RSC could not prevent a rollover. This gave the second piece of necessary information for the conflict—how much faster than the actual FOT speed would the driver have had to enter the maneuver to roll the truck, had the truck been equipped with the RSC. In the maneuver of Figure 1, the driver would have had to begin the maneuver at 24.5 mph, 7.5 mph faster than the driver actually did in the FOT, to overcome the benefit of the RSC and roll the vehicle.

This simulation procedure was repeated for 126 of the 137 conflicts identified in the FOT. (The trailer was empty in the remaining 11 events and not in danger of rolling over, so they were excluded from this analysis.) The simulation exercise produced two data points for each of the 126 maneuvers. The first point is how much faster the driver would need to drive to roll the truck without the RSC (4.8 mph in the illustrated case), and the second is how much faster the driver would need to drive to roll the truck with the RSC (7.5 mph in the illustrated case). These data are tabulated in Appendix A.

In the 125 situations simulated, the RSC always intervened at a speed lower than the speed at which the unequipped truck would roll over. There were no cases where the truck rolled without triggering the RSC. The computer simulation's steering algorithm was developed for following smooth paths, and it does not have all the skills of a human driver to maintain stability of the vehicle in emergency handling situations. The algorithm occasionally responds inappropriately to the sudden braking applied by the RSC. This is why there are a few cases (e.g., case Tractor 4, Trip 685, Identifier 515 – page 21) where the probability of a crash was estimated to be higher with the RSC than without it. A human driver may have responded safely in these circumstances, but that question could not be pursued in the current study.

This example illustrates how the severity of a single conflict was characterized for two conditions—trucks with and without the RSC. The next section shows how these results were used to compute how the RSC reduces the probability of a crash and, from there, how many rollovers it can be expected to prevent.

5.0 Benefits Assessment

In order to determine the potential benefit of implementing the improved RA& C nationwide, the research team examined national crash statistics. The USDOT keeps statistics on the number of truck crashes, the events that precede them, and the number of resulting injuries and fatalities. Data for this project were taken from the General Estimates System (GES) and Fatality Analysis Reporting System (FARS) for the years 1995 through 2000. These data were analyzed and compared to the relatively small amount of data from the FOT and simulations to predict how many crashes could be avoided if the system were deployed nationwide.

5.1 Probability Estimates

The results of the simulations can be used to calculate the probability of a crash for the conflicts, which is a step toward estimating the overall benefits of the system.

Using simulations such as those just illustrated, the probability that each conflict would result in a crash was estimated, using the following equation:

(1)

where indicates conflict number j,

is the probability of a crash resulting from conflict j

is the increase in speed of conflict j that results in a rollover,

is the speed during the FOT of conflict j at the peak lateral acceleration, and

is the Gaussian cumulative distribution.

The scaling factor, , was estimated to be 0.0010 in the independent evaluation [Battelle, 2003, pages 5-36 through 5-40]. As an example, Equation 1 can be applied to the conflict that served as an example in the previous section,

. (1a)

The numerator in this equation, 4.8 mph, is the speed increment required for this maneuver to lead to a rollover. It was estimated by the simulation following the steps illustrated in Section 4.4. The value of 0.0010 is the variance scaling factor, and 1.1 is a units conversion factor [4] . The final value in the denominator, 18.2 mph, is the speed of the vehicle, measured during the FOT, at which the lateral acceleration of the tractor’s steer axle reached a peak value. This quantity was read from one of the “input” columns of Appendix A. The probability of this conflict resulting in a crash even without the RSC is extremely small. Indeed, crashes are rare events, so the probabilities are expected to be remote, and this conflict is among the least likely to result in a rollover.

The second set of simulations, those where the truck was equipped with the RSC, yielded a second set of speed increments, . The formula in Equation (1) was computed again to determine the probability that a truck equipped with RSC would crash, given that it entered one of the 126 conflicts observed in the FOT. Again as an example, Equation 1 can be applied to this same conflict to calculate the probability of a crash given this conflict and that the truck is equipped with RSC:

. (1b)

Thus, there were two numbers for each conflict—the probability of a truck without RSC rolling over and the probability of a truck with RSC rolling over. These pairs of probabilities are tabulated in Appendix A.

The difference between these probabilities is the reduction in probability of a crash that is attributable to the RSC. With the appropriate scaling factors, the probabilities can be summed to determine the total probability of a crash, and multiplied by the number of miles driven by a given fleet, to estimate the number of rollovers the RSC will prevent.

5.2 Benefits Formula

The safety benefit of a countermeasure system is the number of crashes it is expected to prevent, when all factors are considered. It is calculated using Equation 5-13 of the independent evaluation final report [Battelle, 2003] or its simpler form, Equation 5-15 of the report,

B = N _wo ´ App ´ Eff. (2)

The first term in the formula is the average number of annual crashes without the system, N _wo, which is available from GES and FARS. The system’s applicability, App, the proportion of crashes it is intended to address, is also calculated from national crash statistics. The effectiveness of the RA& C was discussed in the evaluation report [Battelle, 2003, Tables 4-2 and 4-3] and in the Task 5.2 report [Battelle, 2003b, Section 2.2]. The efficacy, Eff, is a measure of how close the system performs its intended function. The efficacy is calculated with data from a field operational test and from simulations. The efficacy depends on two quantities, which are termed the prevention ratio and the exposure ratio,

Eff = 1 - PR ´ ER. (3)

The prevention ratio and the exposure ratio were mathematically defined in the evaluation report [Battelle, 2003, Equations 5-1 and 5-6]. Essentially, the exposure ratio measures the ability of the countermeasure system to prevent critical conflicts from happening, and the prevention ratio measures the ability of the countermeasure system to prevent a crash given that a conflict has occurred.

The primary component evaluated in the FOT was the RSA. The advisor, a driver education tool, is expected to reduce the number of times the driver makes a risky, near-rollover maneuver. It can be expected to affect the exposure ratio more than the prevention ratio. Calculations estimate that the RSA alone will prevent about 33 percent of the conflicts involving high speeds in turns that may result in trailer rollovers. This reduction in conflict rates was statistically significant. For the present analysis, the RSA is assigned a prevention ratio of 1.0. [5]

The controller's main benefit is to reduce the probability of a rollover after the vehicle enters a conflict. Therefore, the analysis assumes that, if the RSC were installed alone without the RSA, drivers would behave exactly the same with the RSC installed as they would without. Mathematically, this implies that the exposure ratio would be 1.0 and that all 137 conflicts observed in the FOT are representative of those that could occur if the RSC were installed alone. [6] This assumption would be true if RSC interventions were sufficiently rare that they do not have the training effect of the RSA advisories, and if drivers, knowing they had an extra safety device, resisted the temptation to drive faster or more recklessly.

Using the simulations of the RSC (controller) as described above, the RSC was estimated to prevent about 53 percent of the rollovers resulting from excessive speed in a curve (i.e., the prevention ratio was estimated to be 1-0.53=0.47). The prevention ratio is estimated as the ratio of the overall probability of a crash with the RSC to the overall probability of a crash without the RSC, both given that a driving conflict has occurred. The overall probability of a crash given a conflict is estimated as the average probability of a crash given the 126 specific conflicts considered as described in the following equation:

(4)

The example illustrated in Section 4.4 is now one of the 126 elements in the sum. The value of Equation (1a) is one of the elements in the denominator, where the probability of a crash without the RSC is summed. The value of Equation (1b) is one of the elements in the numerator.

To estimate the combined effect of using both the RSA and RSC, we assume that the RSA would prevent some near-rollover situations from occurring, and that the RSC would prevent some of those that remain from actually leading to a rollover, and that the two effects would be independent of one another. Mathematically, because of the RSA, the exposure ratio would be 0.67, and because of the RSC, the prevention ratio would be 0.47. The combined efficacy is

Eff = 1 - PR ' ER (5)

= 1 - .47 ' .67

= .69.

Therefore, the combined RA& C is estimated to prevent 69 percent of heavy vehicle rollovers that are caused by excessive speed in a turn.

5.3 Number of Rollovers Prevented

The analysis predicted what would happen if the RA& C were applied to four types of fleets nationwide:

• Tractors pulling tank trailers that display a hazardous material placard
• Tractors pulling any tank trailer
• Tractors pulling at least one trailing unit (almost always a semi-trailer)
• All heavy trucks (Class 3 through 8, or 10,000 lb and greater).

One significant finding of this undertaking was that the RSA can be expected to prevent a number of run-off-road (or single-vehicle roadway departure) crashes as well as rollovers. Many run-off-road crashes follow the same pattern as most rollovers—taking a curve too fast. Not as high a fraction of run-off-road crashes involve excessive speed in curves, but because there are many more of them than rollovers, the RA& C is actually expected to prevent more run-off-road incidents than rollover crashes.

In order to apply the results of the FOT, which involved one kind of vehicle in one type of business in one geographical area, some assumptions were made. For the purpose of calculation, the devices were assumed to be deployed throughout the fleets. Applying these results to the four fleet types examined as well as single-vehicle road departures yields the crash avoidance results shown in Table 4. The crash populations in this table are taken from Battelle [2003, Table 5-8, page 5-56; and 2003b, Table 4-1, page 24].

Table 4. Crash Prevention Estimates

5.4 Effect of Circumstances on Performance

The 137 critical conflicts identified in the FOT data occurred in a variety of road geometries, and they represent a variety of vehicle speeds and road curvatures. As these events occurred naturally during the FOT period, they constitute a representative sample of circumstances of possible rollovers, but not an exhaustive study of all circumstances of possible rollovers. The variety provided by these driving conflicts presents the opportunity to explore the question of whether the circumstances of the maneuver affect the performance of the RSC. To do so, the prevention ratios of individual events were considered as a function of four possible independent variables: road geometry, vehicle speed at the time of maximum lateral acceleration, path curvature at the time of maximum lateral acceleration, and vehicle fill (i.e., partial vs. full).

The prevention ratio for an individual driving conflict (PR_j) is calculated as the ratio of the probability of that driving conflict resulting in a crash with the RSC to that same probability without the RSC. Specifically,

(6)

where is calculated as described in Equation 1 and the subscripts w and wo denote the conditions with the RSC and without the RSC, respectively. The probabilities in Equation 6 are functions of , the increase in speed of conflict j that results in a rollover, with and without the RSC. Due to the non-linear nature of Equation 1, it is necessary to explore the prevention ratio directly; exploration of change in increase in conflict speed resulting in a rollover crash ( ) is not sufficient. This is problematic because the probabilities that individual conflicts result in a crash, which are intermediate quantities in the calculation of the prevention ratio, are very small quantities. These quantities vary from each other by orders of magnitude. [7]

Note that 93 of the 126 driving conflicts exhibit improvement due to the RSC, as measured by the increase in change of conflict speed resulting in a rollover crash; 8 exhibit detriment due to the RSC; and 25 exhibit no change.

There are cases where the RSC had an effect as measured by the change in speed increment but no effect as measured by the change in probability of a crash.[8] There were only 37 cases that exhibit measurable improvement due to the RSC as measured by the prevention ratio, 7 that exhibit measurable detriment, and 81 that exhibit no change. Thus, using either measure (change in speed increment or change in crash probability), a safety improvement due to the RSC is indicated. However, there is little data with which to explore factors associated with improvement using the prevention ratio.

The prevention ratio is characterized by a few influential values (i.e., values that are orders of magnitude larger than the rest). Due to these driving conflicts with large values, there is significant variability associated with comparisons made using this data. Sometimes influential values (outliers) are removed from a data set before analysis. This did not make sense in this case, because these are the exact driving conflicts that are most influential in the prevention ratio estimate made in the independent evaluation [Battelle, 2003]. Additionally, when the most extreme outliers are removed from this data set, new observations appear as outliers within the reduced data set; thus, it is difficult to decide exactly how many of these can be reasonably thrown out before analysis. Due to the variability observed in the prevention ratio values, no significant effect due to road geometry, vehicle speed at the time of maximum lateral acceleration, path curvature at the time of maximum lateral acceleration, or vehicle fill (i.e., partial vs. full) could be identified.

6.0 References

Allen, R. W., Szostak, H. T., Klyde, D. H., Rosenthal, T. J., and Owens, K. J., 1992 "Vehicle Dynamic Stability and Rollover," DOT-HS-807 956, September 1992.

Battelle, 2003, "Final Report – Evaluation of the Freightliner Intelligent Vehicle Initiative Field Operational Test," Contract No. DTFJ61-96-C-00077, Task Order 7718.

Battelle, 2003a, "Final Report – Evaluation of the Freightliner Intelligent Vehicle Initiative Field Operational Test," Contract No. DTFJ61-96-C-00077, Task Order 7718, Appendices Volume, Appendix D.

Battelle, 2003b, "Review of Commercial Motor Vehicle Crash Data," Contract DTFH61-96-C-00077, Task Order 32.

Battelle, 2003c, "Analysis and Documentation of Industry Benefits and Costs for the Improved Roll Advisor and Controller Technology," Contract DTFH61-96-C-00077, Task Order 32.

Appendix A

Input and Output Data in Tabular Format

The VDANL model inputs and outputs are summarized in the following table for each critical event analyzed. Each row in the following table represents one conflict that was studied. The first three columns identify the conflict; the next four describe the condition of the conflict; and the final six present the results of either the simulation study or the statistical analysis.

Tractor, Trip, and Identifier in the first three columns of the table uniquely identify a conflict. The input values, dynamic output values, and crash probability are described below.

Input Values

Initial Speed: This is the speed measured on the truck during the FOT. It was recorded at the time of the peak in the lateral acceleration, measured by the accelerometer mounted on the steer axle of the tractor.

Curvature: The simulation path curvature at instant of maximum tractor acceleration. This is not the road curvature. As the vehicle is maneuvering to maintain a path in a severe roll, this curvature may be significantly different from the road curvature. A positive value indicates a left turn and a negative value, a right turn.

Loading Condition: The trailer loading condition – full or partial. Vehicles with a nearly full load at the time of the conflict (36 to 41 tons) were simulated with a vehicle weight of 40 tons. Vehicles with a partial load at the time of the conflict (26 to 35 tons) were assigned a weight of 31 tons in the simulation. See Table 2 of the text and the accompanying discussion. All vehicles in the FOT were Class 8 tractors pulling liquid nitrogen trailers, and all vehicles in the simulation were five-axle articulated vehicles.

Curve Shape: Gives a description of the type of curve being negotiated. Corresponds to the descriptions in Appendix B.

Dynamic Output Values

The output columns have data sorted by whether the RSC was active or not active. They were calculated when the vehicle was simulated as going faster than in the FOT.

Speed at Rollover: The speed when the “initial speed” had been increased sufficiently to lead to a rollover. This first column is the maximum speed at which the maneuver could be taken without rolling over, when the RSC was not present. The second column is the maximum speed at which the RSC can prevent a rollover.

Trailer Acceleration: The lateral acceleration of the trailer at the instant of maximum tractor lateral acceleration. The simulation was conducted at the speed where the vehicle is predicted to roll over without the RSC. The cases with RSC were simulated beginning at the same speed as those without the RSC, but the RSC activated and changed the dynamics at the point of near-rollover. When the peak lateral acceleration is lower in the case with the RSC, it indicates that the RSC has reduced the rollover tendency of the trailer. (A positive value indicates a left turn and a negative value, a right turn.)

Speed Increment to Crash and Crash Probability

Speed Increment to Crash: This is how much faster than the original FOT speed the vehicle would have to traverse the path to roll the vehicle. These speed increments are the change in speeds used to calculate the probability of a crash in Equation (1) of the main text.

Probability of a Crash: These columns indicate the probability of a rollover crash, given that the respective conflict occurred. These probabilities are summarized and combined to calculate the Prevention Ratio as in Equation (3) of the text. Because the probabilities vary over a wide range, they are expressed as a phrase instead of a number. For example, if the probability is listed as, “one in a . . . million,” that means that the probability of a crash is approximately 10^-6, or that if this same conflict were repeated a million times, each with slightly different perturbations, one of them would be expected to roll over. A blank entry indicates that the probability of a crash was quite remote, less than one in a billion.

The highlighted row, for Tractor 4, Trip 1072, and identifier 622 – page 24, is the one illustrated in Figures 1 through 4 of the text.

VDANL Model Inputs and Outputs