A Simulation Approach to Estimate 

the Efficacy of Meritor WABCO’s 

Improved Roll Stability Control 

October 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) 

1. Report No. 

 FMCSA-MCRR -06-006 

2. Government Accession No. 3. Recipient's Catalog No. 

4. Title and Subtitle: 

A Simulation Approach to Estimate the Efficacy 

Stability Control 

of Meritor WABCO’s Improved Roll 

5. Report Date: 

 October 2006 

6. Performing Organization Code 

7. Author(s): 

Amy Houser (FMCSA), Douglas Pope (Battelle Memorial Institute), Nancy McMillan 

(Battelle Memorial Institute) 

8. Performing Organization Report No 

9. Performing Organization Name and Address: 10. Work Unit No. 

Battelle Memorial Institute 

505 King Avenue 

Columbus, OH 43201-2693 

11. Contract or Grant No. 

Contract DTFH61-96-C-00077 

12. Sponsoring Agency Name and Address: 

Federal Motor Carrier Safety Administration 

Office of Research and Analysis 

400 Virginia Avenue, SW, Suite 600 

Washington, DC 20024 

13. Type of Report and Period Covered 

 Final Report, August 2001 – May 2006

14. Sponsoring Agency Code 

FMCSA 

15. Supplementary Notes: 

The Contracting Officer’s 

 

Technical Representative was Amy Houser, FMCSA Office of Research and Analysis 

16. Abstract: 

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 US 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, 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). 

• 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. 

17. Key Words: 

On-board Safety System, Roll Stability Advisor, Roll Stability Control, Rollover 

18. Distribution 

No restrictions 

Statement 

19. Security Classif. (of this report) 

 Unclassified 

20. Security Classif. (of this page) 

 Unclassified 

21. No. of Pages: 

48 

22. Price 
SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS FRO

Symbol When You Know Multiply By To Find Symbol Symbol When You Know Multiply By 

LENGTH LENGTH

in ftydmi

inches 25.4 millimeters 

 feet 0.305 meters 

 yards 0.914 meters 

 miles 1.61 kilometers 

AREA 

mm 

m 

m 

km 

mm

m 

m 

km 

 millimeters 0.039 inc

meters 3.28 fee

meters 1.09 Ya

kilometers 0.621 mi

AREA

in2

ft2

yd2

ac mi2

fl oz gal ft3yd3

oz lbT °F fc fllbf psi 

square inches 645.2 square millimeters 

 square feet 0.093 square meters 

square yards 0.836 square meters 

acres 0.405 hectares 

 square miles 2.59 square kilometers 

VOLUME 

fluid ounces 29.57 milliliters 

gallons 3.785 liters 

 cubic feet 0.028 cubic meters 

cubic yards 0.765 cubic meters 

MASS 

ounces 28.35 grams 

 pounds 0.454 kilograms 

short tons (2000 lbs) 0.907 megagrams 

TEMPERATURE (exact) 

Fahrenheit 5(F-32)/9 Celsius 

 temperature or (F-32)/1.8 temperature 

ILLUMINATION 

foot-candles 10.76 lux 

 foot-Lamberts 3.426 candela/m2 

FORCE and PRESSURE or STRESS 

pound-force 4.45 newtons pound-force 6.89 kilopascals per square inch 

2 mm

2 m2 m

ha 

km2

ml 

l 

3 m3 m

g 

kg 

Mg 

°C 

lx 

cd/m2 

N 

kPa 

2 mm

2 m2 m

ha 

 km2

ml 

l 

3 m3 m

g 

kg 

Mg °C lx

cd/m2 

N kPa 

square millimeters 0.0016 squ

 square meters 10.764 squ

square meters 1.195 squ

hectares 2.47 acr

 square kilometers 0.386 squ

VOLUME

milliliters 0.034 flu

liters 0.264 ga

 cubic meters 35.71 cu

cubic meters 1.307 cu

MASS

grams 0.035 ou

kilograms 2.202 po

megagrams 1.103 sho

TEMPERATURE (exac

Celsius 1.8 C + 32 

temperature 

ILLUMINATION

 lux 0.0929 

candela/m2 0.2919 

FORCE and PRESSURE or S

newtons 0.225 

kilopascals 0.145 

* SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380.
i 

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 

Table of Contents 
ii

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 onboard 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 

1
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 

 

1

 The VDANL model, including the equations of motion, is documented in Allen, R.W., Szostak, H.T., Klyde, D.H., 

Rosenthal, T.J., and Owens, K.J., Vehicle Dynamic Stability and Rollover, DOT-HS-807 956, September 1992. 

2
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 

 

2

 VDANL, Systems Technology Inc., Hawthorne, CA. Phone 310-679-2281. 

3
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 

Sprung Mass 

Center of 

Whole Unit 

Center of Track 

Vehicle Component Mass Gravity Height Gravity Height Wheelbase Width 

Tractor 16,600 lb 2.92 ft 3.34 ft 15.5 ft 7.5 ft 

Trailer (partial load) 45,000 lb 5.7 ft 6.1 ft 34.0 ft 7.5 ft Trailer (full load) 64,100 lb 7.1 ft 7.36 ft 

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 

Condition of the 

Vehicle in the Conflict 

in the FOT 

Number of 

Conflicts 

Range of Vehicle 

Weights Measured 

in the FOT 

Vehicle Weight in the 

Corresponding 

VDANL Model 

Full or nearly full 113 36 to 41 tons 40 tons 

Partially loaded 13 26 to 35 tons 31 tons 

Empty or nearly empty 11 17 to 24 tons -- 

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. 

4
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 

5
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 

Condition 

Peak Deceleration, g 

Actual Vehicle at TRC, VDANL Model of 

equipped with RSC vehicle with RSC 

full vehicle, high risk 0.22 0.24 

full vehicle, moderate risk 0.12 0.125 

partially loaded vehicle, moderate risk 0.12 0.12 

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 

 

3

 The FOT had two phases. Of the 137 conflicts, 71 came from the first phase and 66 from the second. The analysis 

in the independent evaluation discerned no significant difference between conflicts from the two phases. Therefore, 

to provide a larger pool for analysis in the present study, all conflicts were studied together without regard to the 

phase in which they originated. 

6
RSC enter a curve at speed perturbations higher than an identical truck without the RSC and not 

roll over). 

Figure 1. Path of the Truck in One of 

the Critical Conflicts 

-1000

-500

0

0 500 1000

ft

ft

location of maximum 

lateral acceleration

travel direction

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

0

10

20

30

40

0 15 30 45

Time, s

Speed, mph

Nearly Rolls Over without RSC

Original Event Speed, from the FOT

18.2 mph

22.3 mph. The next increment is 

23.0 mph, where the truck rolls

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 

7
8

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. 

0

10

20

30

40

0 15 30 4

Time, s

Speed, mph

Without RSC

RSC intervention With RSC

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

5
-0.4

-0.2

0.0

0.2

0.4

0 15 30 45

Time, s

Lateral Acceleration, g

without RSC

with RSC

Figure 4. RSC Limits the Lateral Acceleration of the Trailer 

-20

-10

0

10

20

0 15 30 45

Time, s

Roll Angle, degrees

Without RSC

With RSC

dangerous trailer roll of 15 ° 

without the RSC

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 

9
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: 

∆v

P(C | S ) 1 ( j,R

1, j = − Φ )

σ × v j,M

 (1) 

where S1, j indicates conflict number j, 

P(C | S1, j ) is the probability of a crash resulting from conflict j 

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

10
v j,M is the speed during the FOT of conflict j at the peak lateral acceleration, and 

Φ() is the Gaussian cumulative distribution. 

The scaling factor,σ , 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, 

∆v j,R 4.8 P(C | S ) 1 ( 14

1, j = − Φ ) = 1− Φ( ) = 1.53×10− . (1a) 

σ × v j,M 0.0010×1.1×18.2

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 

factor4

. 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, ∆v′

j,R . 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: 

∆v

P(C | S ) = 1− Φ( j,R 7.5

1, j ) = 1− Φ( ) ≈ 0 . (1b)

σ × v j,M 0.0010×1.1×18.2

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. 

 

4

 The scaling factor σ itself is nondimensional. The FOT Evaluation was conducted mostly in metric units, but the 

present report is in English units. The difference in units between reports requires the units conversion factor. 1ft/s 

≈ 1.1 kph. 

11
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 = Nwo × App × Eff. (2) 

The first term in the formula is the average number of annual crashes without the system, Nwo,

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 

 

5

 The original evaluation report [Battelle, 2003, pages 5-43 to 5-45] estimated the prevention ratio to be 1.2; that is, 

the conflicts occurring with the RSA are, on average, slightly more severe than those without. The efficacy of the 

RSA was estimated to be 20 percent (1-1.2×0.67). However, for the present analysis, the prevention ratio is taken to 

be 1.0, and the RSA (advisor) acting alone is estimated to prevent about 33 percent (1-1.0×0.67) of rollover crashes 

involving high speeds in turns. This is because (a) the estimated RSA prevention ratio of 1.2 was not statistically 

significant, and (b) the RSC, which intervenes when rollover is believed to be imminent, is expected to play the 

dominant role in reducing the number of near-rollover maneuvers that actually lead to rollover. 

6

 An earlier version of the RSC was installed in the vehicles in the FOT. It activated only a few times during the 

FOT and in only 11 cases did it affect the vehicle dynamics. Not once did the drivers recognize the RSC 

12
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: 

1 126

P (C | S

P (C | S ) ∑ 126 w 1,i)

PR = w 1 = i=1 = 0.53

Pwo (C | S1 ) 1 ∑

126

P 1, 126 wo (C | S i)

i=1 (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 

 

intervention. Therefore, we feel justified in our assumption that the RSC’s presence did not appreciably affect the 

behavior of the drivers of the FOT. 

13
• 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 

Type of Truck 

Rollover (Fast Turn)

Number of Trucks in 

Crashes/Year

Number of Crashes Avoided

RSA (33%) RSC (53%) RA&C (69%)

HazMat Tankers 4 1.4 2.3 3

All Tankers 46 15 24 32

Tractor Trailers 471 155 250 325

Large Trucks 787 260 417 543

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 (PRj) 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, 

P ( | w C S1, j ) PRj = (6) Pwo (C | S1, j )

14
where P(C | S1, j ) 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∆v j,R , 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 

(∆v j,R − ∆v′

j,R ) 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. 

 

7

 There were some conflicts where the RSC reduced the probability of a crash, but the probability of a crash was 

already very low, even without the RSC. A good example is the second entry in the table in Appendix A. The 

probability of that conflict becoming a rollover crash without the RSC is one in a hundred million. With the RSC, 

the probability of a crash is more remote than one in a billion. That is an improvement, but it does not significantly 

affect the overall probability because, for example, in the first and third conflicts in the table are a hundred times 

more likely to result in a crash than is the second entry. 

8

 The second entry in the table of Appendix A is an example of a “measurable” improvement. The probability of a 

crash is substantially lower with the RSC than without. The fifth entry in the table is an example of a change that 

cannot be measured. The probability of a crash is approximately one in a billion, regardless of whether the RSC is 

present. 

15
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-C00077, 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.

16
Appendix A 

Input and Output Data in Tabular Format
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 

 18 
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 nearrollover. 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 

∆v speeds j,R 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.

 19 
20 

VDANL Model Inputs and Outputs 

Identification Input Output Im

Tractor Trip Identifier 

FOT 

Speed 

mph 

Curvature 

1/ft 

Loading 

Condition Curve Shape 

Without 

RSC 

With 

RSC 

Without 

RSC 

With 

RSC 

Without 

RSC 

Speed of the 

Rollover 

Simulation 

mph 

Trailer 

Max. Accel. 

g 

Speed I

to Ro

m

1 407 595 29.8 0.008 Full ? Turns 34.5 35.9 0.38 0.36 4.8 

1 780 696 28.4 0.008 Full ? Turns 33.9 35.9 0.47 0.43 5.5 

1 1179 580 28.0 0.007 Full ? Turns 32.7 34.8 0.38 0.38 4.8 1 1678 511 29.5 0.008 Full ? Turns 35.0 35.7 0.47 0.41 5.5 

2 1244 420 27.0 0.009 Full ? Turns 32.4 32.4 0.39 0.44 5.5 

3 77 578 29.6 0.007 Full ? Turns 35.7 36.4 0.43 0.38 6.1 

3 568 700 27.9 0.009 Full ? Turns 33.3 33.3 0.46 0.41 5.5 

4 1224 751 29.8 0.008 Full ? Turns 33.9 33.9 0.39 0.40 4.1 

4 1312 510 27.9 0.008 Full ? Turns 32.7 35.4 0.39 0.37 4.8 5 271 471 29.8 0.008 Full ? Turns 34.5 35.2 0.39 0.38 4.8 

5 1728 496 28.7 0.008 Full ? Turns 33.5 32.8 0.40 -- 4.8 

6 282 634 29.4 0.007 Full ? Turns 34.2 34.9 0.46 0.35 4.8 

1 1693 381 22.8 0.009 Full Consecutive Opposite Turns 30.3 34.4 0.42 0.35 7.5 2 758 474 20.5 -0.009 Full Consecutive Opposite Turns 25.2 29.3 0.32 -0.29 4.8 

2 811 523 15.8 -0.015 Full Consecutive Opposite Turns 20.6 19.2 -0.38 -- 4.8 

2 1468 558 15.7 -0.016 Full Consecutive Opposite Turns 19.1 22.5 -0.31 -0.30 3.4 

3 83 425 16.0 0.014 Full Consecutive Opposite Turns 21.4 22.8 0.32 0.32 5.5 

3 98 551 16.5 -0.016 Full Consecutive Opposite Turns 19.2 19.2 -0.34 -0.34 2.7 
VDANL Model Inputs and Outputs 

21 

Identification Input Output Im

Without 

RSC 

With 

RSC 

Without 

RSC 

With 

RSC 

Without 

RSC 

Tractor Trip Identifier 

FOT 

Speed 

mph 

Curvature 

1/ft 

Loading 

Condition Curve Shape Speed of the Rollover 

Simulation 

mph 

Trailer 

Max. Accel. 

g 

Speed I

to Ro

m

3 276 414 15.9 -0.013 Full Consecutive Opposite Turns 20.0 20.0 0.31 -0.31 4.1 3 1211 310 16.6 -0.011 Full Consecutive Opposite Turns 20.1 22.8 -0.36 -0.29 3.4 4 623 397 16.8 -0.017 Full Consecutive Opposite Turns 22.9 25.0 0.41 0.29 6.1 4 685 515 16.1 -0.022 Full Consecutive Opposite Turns 22.9 18.8 0.15 -- 6.8 5 26 568 16.6 -0.016 Full Consecutive Opposite Turns 19.3 20.0 -0.31 -0.30 2.7 5 526 635 15.1 -0.014 Full Consecutive Opposite Turns 19.2 19.9 -0.34 0.26 4.1 5 922 331 20.2 -0.010 Full Consecutive Opposite Turns 23.6 26.4 -0.36 -0.33 3.4 5 1304 421 16.0 -0.015 Full Consecutive Opposite Turns 19.4 19.4 -0.32 -0.32 3.4 6 523 446 15.9 -0.013 Full Consecutive Opposite Turns 20.7 23.4 -0.34 -0.33 4.8 3 508 250 34.9 0.005 Full Gradual Left 56.0 55.3 0.57 -- 21.1 3 1052 427 38.9 0.005 Full Gradual Left 59.3 59.3 -0.56 0.71 20.5 1 777 416 15.4 0.014 Full Left Turn 20.2 20.2 0.33 0.33 4.8 2 360 787 15.9 0.023 Full Left Turn 28.2 19.3 0.08 -- 12.3 2 549 623 15.7 0.017 Partial Left Turn 20.5 27.3 0.42 0.35 4.8 2 1839 522 16.4 0.015 Full Left Turn 19.2 19.2 0.32 0.32 2.7 2 1844 356 16.3 0.012 Full Left Turn 22.4 23.8 0.07 0.35 6.1 3 877 395 17.8 0.013 Full Left Turn 21.2 22.6 0.31 0.29 3.4 3 1308 475 16.7 0.012 Full Left Turn 20.8 27.6 0.36 0.34 4.1 4 449 444 15.8 0.017 Partial Left Turn 21.2 30.8 0.44 0.39 5.5 4 1548 443 16.1 0.015 Full Left Turn 20.2 22.3 0.32 0.31 4.1 4 1608 629 16.7 0.012 Full Left Turn 22.8 24.9 0.33 0.31 6.1 4 1665 549 16.2 0.011 Full Left Turn 21.6 23.0 -0.31 0.32 5.5 
VDANL Model Inputs and Outputs 

Identification Input Output Im

Tractor Trip Identifier 

FOT 

Speed 

mph 

Curvature 

1/ft 

Loading 

Condition Curve Shape 

Without 

RSC 

With 

RSC 

Without 

RSC 

With 

RSC 

Without 

RSC 

Speed of the 

Rollover 

Simulation 

mph 

Trailer 

Max. Accel. 

g 

Speed I

to Ro

m

4 1682 674 18.2 0.010 Full Left Turn 23.0 25.0 0.34 0.34 4.8 

5 89 441 15.7 0.018 Full Left Turn 19.1 19.1 0.33 0.32 3.4 

5 126 376 15.7 0.016 Full Left Turn 20.4 23.2 0.37 0.35 4.8 

5 229 470 16.0 0.015 Partial Left Turn 24.9 29.7 0.48 0.33 8.9 

6 306 358 16.9 0.016 Full Left Turn 20.3 21.6 0.34 0.34 3.4 

6 454 535 15.2 0.021 Partial Left Turn 18.6 17.2 0.42 -- 3.4 1 766 774 19.7 -0.011 Full Right Turn 25.8 29.9 -0.36 -0.32 6.1 2 1155 466 20.4 -0.009 Full Right Turn 25.9 27.9 -0.35 -0.31 5.5 

3 508 259 16.2 -0.014 Full Right Turn 19.6 19.6 -0.32 -0.32 3.4 3 1053 534 17.7 -0.009 Full Right Turn 21.8 21.1 -0.31 -- 4.1 

3 1211 310 19.0 -0.013 Full Right Turn 23.8 25.8 -0.35 -0.35 4.8 

3 1566 261 15.9 -0.013 Full Right Turn 19.3 19.3 -0.33 -0.33 3.4 

4 865 832 16.1 -0.014 Full Right Turn 21.6 21.6 -0.35 -0.33 5.5 

4 1566 670 16.1 -0.017 Full Right Turn 18.9 19.5 -0.30 -0.30 2.7 

1 418 620 16.6 -0.015 Full S-Curve 22.1 23.4 -0.36 0.28 5.5 

1 974 367 17.2 0.013 Full S-Curve 23.4 27.5 0.36 0.33 6.1 1 1000 361 19.3 -0.009 Full S-Curve 26.8 30.2 -0.37 0.30 7.5 

1 1228 504 17.2 0.011 Full S-Curve 23.4 26.1 0.35 0.28 6.1 

2 1143 313 17.8 -0.011 Full S-Curve 24.7 27.4 -0.34 0.30 6.8 

2 1616 508 15.7 -0.017 Partial S-Curve 21.8 25.2 -0.43 0.36 6.1 

3 551 380 19.5 -0.011 Full S-Curve 26.3 27.7 -0.37 0.31 6.8 

4 887 377 17.4 0.011 Full S-Curve 25.6 26.9 0.37 0.33 8.2 

4 1115 535 17.8 -0.013 Full S-Curve 

S-Curve 

23.2 25.3 -0.35 0.31 5.5 

5 76 497 20.0 0.013 Full 25.5 27.5 0.34 0.30 5.5 

5 127 416 15.8 -0.012 Full S-Curve 22.0 26.1 -0.35 -0.32 6.1 

5 1202 537 17.8 0.018 Partial S-Curve 25.3 32.8 0.46 0.38 7.5 

22
VDANL Model Inputs and Outputs 

23 

Identification Input Output Im

Tractor Trip Identifier 

FOT 

Speed 

mph 

Curvature 

1/ft 

Loading 

Condition Curve Shape 

Without 

RSC 

With 

RSC 

Without 

RSC 

With 

RSC 

Without 

RSC 

Speed of the 

Rollover 

Simulation 

mph 

Trailer 

Max. Accel. 

g 

Speed I

to Ro

m

5 1630 560 16.8 -0.018 Full S-Curve 18.1 21.6 -0.34 0.29 1.4 

6 459 396 21.0 -0.012 Full S-Curve 28.5 31.3 -0.37 0.28 7.5 6 1139 447 17.0 -0.014 Full S-Curve 21.8 23.1 0.38 0.28 4.8 

1 605 267 15.8 0.016 Partial Sharp Trumpet Turn 22.6 29.4 0.44 0.36 6.8 1 1516 560 16.9 0.012 Full Sharp Trumpet Turn 22.3 23.7 0.35 0.33 5.5 

1 1680 282 16.8 0.013 Full Sharp Trumpet Turn 20.9 23.0 0.32 0.32 4.1 

2 633 410 18.2 -0.004 Full Sharp Trumpet Turn 23.7 24.4 0.33 0.32 5.5 

2 634 444 17.7 0.014 Partial Sharp Trumpet Turn 25.9 32.7 0.48 0.35 8.2 

3 1412 425 17.2 0.016 Partial Sharp Trumpet Turn 24.0 29.4 0.44 0.34 6.8 

3 1735 452 18.1 0.012 Full Sharp Trumpet Turn 22.2 26.3 0.34 0.32 4.1 

4 653 630 15.8 0.022 Partial Sharp Trumpet Turn 19.2 26.7 0.47 0.32 3.4 4 811 336 16.1 0.015 Full Sharp Trumpet Turn 19.6 20.2 0.35 0.33 3.4 

5 1298 384 15.5 -0.015 Partial Sharp Trumpet Turn 20.9 32.5 -0.44 -0.37 5.5 6 911 605 17.2 0.014 Full Sharp Trumpet Turn 21.3 22.6 0.32 0.31 4.1 4 790 564 18.4 -0.011 Full Slight Right at Stop 27.9 27.9 -0.33 -0.34 9.5 

4 1259 565 17.2 -0.013 Full Slight Right at Stop 27.4 27.4 -0.33 -0.33 10.2 

4 1540 609 18.6 -0.012 Full Slight Right at Stop 28.1 28.8 -0.35 -0.34 9.5 

5 1011 481 15.7 -0.013 Full Slight Right at Stop 26.0 26.6 -0.35 -0.33 10.2 

6 1122 563 16.5 -0.013 Full Slight Right at 26.7 26.7 -0.34 -0.33 10.2 
VDANL Model Inputs and Outputs 

24 

Identification Input Output Im

Tractor Trip Identifier 

FOT 

Speed 

mph 

Curvature 

1/ft 

Loading 

Condition Curve Shape 

Without 

RSC 

With 

RSC 

Without 

RSC 

With 

RSC 

Without 

RSC 

Speed of the 

Rollover 

Simulation 

mph 

Trailer 

Max. Accel. 

g 

Speed I

to Ro

m

Stop 

3 256 641 29.9 -0.010 Full Turn Over 180 34.7 34.7 -0.36 -0.43 4.8 

3 877 335 28.9 -0.006 Full Turn Over 180 34.3 34.3 -0.39 -0.33 5.5 5 707 316 18.4 -0.013 Full Turn Over 180 22.5 25.9 -0.35 -0.35 4.1 

1 397 471 18.2 0.011 Full Unique Curve 26.4 27.1 0.33 0.33 8.2 1 676 622 24.1 -0.008 Full Unique Curve 34.3 35.7 -0.47 -0.45 10.2 

1 690 635 24.2 -0.006 Full Unique Curve 34.4 35.1 -0.40 -0.42 10.2 

1 787 489 51.7 -0.005 Full Unique Curve 64.0 62.6 -0.47 -- 12.3 

1 965 908 19.8 0.009 Full Unique Curve 27.3 30.7 0.37 0.31 7.5 

1 1043 461 17.7 -0.006 Full Unique Curve 29.3 29.9 -0.41 -0.40 11.6 1 1084 569 16.6 0.011 Full Unique Curve 23.4 25.4 0.38 0.31 6.8 

1 1119 508 17.1 0.014 Full Unique Curve 21.9 23.9 0.38 0.33 4.8 

1 1571 420 15.5 0.014 Full Unique Curve 20.3 20.3 0.32 0.33 4.8 

1 1687 569 17.1 0.005 Full Unique Curve 22.6 24.0 0.39 0.38 5.5 

3 332 616 41.2 -0.005 Full Unique Curve 50.0 50.0 -0.58 -0.48 8.9 

3 508 298 16.8 0.014 Full Unique Curve 22.2 25.0 0.33 0.34 5.5 

3 813 415 16.0 0.011 Full Unique Curve 21.4 22.8 0.37 0.35 5.5 3 850 368 16.1 0.015 Full Unique Curve 18.1 18.8 0.32 0.31 2.0 

3 1660 431 16.1 0.013 Full Unique Curve 20.1 24.2 0.32 0.30 4.1 

4 480 565 20.3 -0.011 Full Unique Curve 25.8 29.2 -0.35 -0.30 5.5 

4 523 497 16.0 -0.020 Full Unique Curve 20.1 20.1 -0.35 -0.35 4.1 

4 1072 622 18.2 -0.014 Full Unique Curve 23.0 25.7 -0.40 -0.30 4.8 

4 1548 437 17.5 -0.014 Full Unique Curve 21.6 25.7 -0.35 -0.32 4.1 

4 1587 445 16.9 0.012 Full Unique Curve 22.4 25.8 0.33 0.34 5.5 

4 1665 549 18.1 -0.013 Full Unique Curve 24.2 25.6 -0.34 -0.33 6.1 

4 1689 622 22.0 -0.009 Full Unique Curve 30.9 32.9 -0.41 -0.36 8.9 
VDANL Model Inputs and Outputs 

25 

Identification Input Output Im

Without 

RSC 

With 

RSC 

Without 

RSC 

With 

RSC 

Without 

RSC 

Tractor Trip Identifier 

FOT 

Speed 

mph 

Curvature 

1/ft 

Loading 

Condition Curve Shape Speed of the Rollover 

Simulation 

mph 

Trailer 

Max. Accel. 

g 

Speed I

to Ro

m

5 86 534 16.1 -0.013 Full Unique Curve 20.9 24.3 -0.38 -0.28 4.8 5 126 375 17.8 -0.013 Full Unique Curve 21.8 28.7 -0.39 -0.34 4.1 5 482 579 15.9 -0.014 Full Unique Curve 20.0 20.0 -0.34 -0.34 4.1 5 688 432 22.1 -0.007 Full Unique Curve 34.4 35.8 -0.45 -0.39 12.3 5 1263 545 17.2 0.010 Full Unique Curve 25.4 27.5 0.36 0.30 8.2 6 128 620 17.9 0.014 Full Unique Curve 24.1 25.4 0.36 0.29 6.1 6 287 708 16.5 0.012 Full Unique Curve 17.8 17.8 0.37 0.36 1.4 6 1090 488 15.8 0.015 Partial Unique Curve 23.3 30.1 0.44 0.34 7.5 6 1222 661 17.1 0.008 Full Unique Curve 20.5 20.5 -0.37 -0.28 3.4 1 787 548 16.9 -0.013 Full Wiggle 26.5 26.5 -0.34 -0.36 9.5 1 800 562 15.8 -0.005 Full Wiggle 26.0 26.7 -0.39 -0.39 10.2 1 1701 645 26.3 0.005 Full Wiggle 42.0 43.4 0.43 0.40 15.7 3 1767 690 16.9 0.010 Full Wiggle 27.1 27.8 0.37 0.34 10.2 5 469 413 17.9 -0.011 Full Wiggle 23.4 25.4 0.34 0.29 5.5 6 177 492 15.8 -0.014 Full Wiggle 25.3 26.7 -0.36 -0.33 9.5 
Appendix B 

Conflict Analysis Plots
 27 

Appendix B 

Conflict Interpretation Example 

In order to interpret individual conflicts, a tool was developed to plot the relevant information 

relating to a conflict. A screen capture of the tool’s output is shown on the following page. This 

group of plots on this page provides the information needed to understand what took place 

during each of the conflicts. 

On each page, the plot in the upper left indicates the lateral acceleration of the vehicle, which is 

often referred to as Ay because it is the acceleration along the y axis perpendicular to the vehicle. 

The plot includes the tractor number (1-6), the trip number, and an identifier for the individual 

conflict. (These three indexes can be used to find the conflict in Appendix A. The first three 

digits of the identifier in this appendix correspond to the identifier in the third column of the 

table in Appendix A.) The plot includes both the lateral acceleration measured at the steer axle 

and the calculated lateral acceleration based on speed and yaw rate. The measured acceleration 

was used in the conflict analysis. 

The two plots in the lower left corner are from the lane tracker that was on the trucks but not an 

official part of the FOT. The uppermost plot on the right side is the speed of the vehicle in 

kilometers per hour. These units can be converted into miles per hour by multiplying kilometers 

by 5/8. 

The plot below the speed plot is the instantaneous path curvature as a function of time. This 

indicates how tight a turn the vehicle was making. Curvature is the inverse of the radius of the 

curve. As a turn gets tighter and its radius of curvature decreases, the curvature increases. In 

both the lateral acceleration and curvature plots, negative values indicate a turn to the right and 

positive values a turn to the left. 

The plot in the lower right is the GPS data recorded by the vehicle during the conflict. It is 

important to note that the conflict always begins at the origin of this plot because, unlike the 

other plots, this plot does not move from left to right over time. This plot provides a bird’s-eye 

view of the vehicle path during the conflict and is very helpful to understand what occurred 

during the conflict. The shapes into which the conflicts are grouped in this appendix and the 

Curve Shape column in Appendix A are characterizations of the shapes in this window. 

Interpretation of the conflict requires relating what is taking place in several plots at the same 

time. A first step is to understand the state of the vehicle at the beginning of the plotted conflict. 

At the beginning of the plots shown on the following page, the vehicle is traveling fairly straight; 

the lateral acceleration and curvature both being near zero. The vehicle is also traveling at a 

relatively high rate of speed (approximately 66 kph or 41 mph), but is decelerating. 
 28 
 29 

The vehicle then makes a right turn while maintaining or slightly increasing its speed. 

This turn is shown in the GPS plot as only a slight turn of less than 90 degrees. The 

vehicle then makes a sustained left turn of nearly constant radius. This turn appears as a 

plateau from roughly 15 s to 30 s in both the lateral acceleration and the curvature plots. 

The speed during this left turn is relatively constant. 

After the sustained left turn, the vehicle travels straight for a short distance. This is 

indicated in the curvature and lateral acceleration plots by a return of the plot to near zero 

values. This straight section occurs from roughly 30 s to 40 s. The speed plot during the 

time shows a slight deceleration of the vehicle. 

The vehicle then makes another left turn, less severe than the previous one, both because 

the vehicle is traveling a little slower at this time as shown in the speed plot, and because 

the turn is not as tight as shown in the curvature plot. Both of these factors influence the 

lateral acceleration which is significantly lower than during the previous left turn. By the 

end of this second left turn which occurs from roughly 40 s to 55 s, the speed of the 

vehicle has decreased significantly. The speed of the vehicle continues to decrease as the 

vehicle straightens out and eventually stops at about 66 s as shown in the speed plot. 

This conflict took place on an off ramp at an interchange as the vehicle was leaving the 

freeway. 

Other items on the figures are not relevant to the present report. At the right of the 

figures, “Weight” is the mass of the total vehicle in metric tons as calculated by the FOT 

partnership. “Wiper Intensity” indicates whether the tractor’s windshield wipers were 

operating at the time of the conflict. A value of 0 means they were off, 1 means they 

were on low speed, and 2 means they were on high speed. A fractional value indicates an 

intermittent setting. “Peak rollover index” is a preliminary measure of the conflicts 

severity, as defined in Equation (4-1) of the FOT evaluation report. The “Visibility” was 

intended to be an indication of weather conditions at the time of the conflict, but the data 

proved to be more difficult to gather than first expected, so the field was not used. The 

“Conflict Number” scroll bar, the two circular indicators in the lower right, and the three 

buttons under the GPS map were all intended for internal use by Battelle in classifying 

the conflicts, and they do not present any information about the conflicts. 
 30 
Appendix C 

VDANL Vehicle and 

Trailer Characterization Data
 32 

Appendix C 

VDANL Vehicle and Trailer Characterization Data 

Several input files are required for using VDANL for simulation of vehicles. These input files 

are described in a particular format and each file contains input information on one or more 

aspects of the vehicle that is being modeled. The standard vehicle and trailer files contain 

information that includes vehicle and trailer sprung and unsprung mass and inertia values, 

wheelbase, track width and center of gravity locations. A detailed description of the input 

parameters required for VDANL can been seen in (Allen, R.W., et al. (1992), “Vehicle 

Dynamics Stability and Rollover,” Final Report on NHTSA Contract DTNH22-88-C-07384). 

The vehicle and trailer input files used in this program have been included in this appendix. The 

vehicle file (Table C-1) remains the same for the fully loaded and partially loaded cases. 

However, the trailer files (Tables C-2 and C-3) are different for the two cases and they are 

reflected in the sprung mass weights, inertias, and the center of gravity locations. 

In addition to the vehicle and trailer files, the other input files are used for defining engine and 

drive train aspects of the vehicle, vehicle tire parameters, and vehicle driver model parameters. 

A complete description of the data parameters are provided in Table C-4. 
 33 

Table C-1. Vehicle Parameters 

V.MASS = 515 

V.SMASS = 350 

V.UMASSF = 35 

V.UMASSR = 130 

V.VLENA = 4.5 

V.VLENB = 11 

V.IXS = 5076 

V.IYS = 16023 

V.IXZ = 0 

V.IZZ = 30000 

V.KSTR = 15.45 

V.KSCF = 0.000038 

V.KSCB = 0 

V.DLADV = 0 

V.DNADV = 0 

V.DYADV = 0 

V.DENSITY = 0.00237 

V.REFAREA = 0 

V.CDX = 0.4 

V.AEROVEL = 44 

V.KSAF = 1 

V.KSAR = 1 

V.KSF = 16000 

V.KSR = 87800 

V.KSDF = 423 

V.KSDR = 864 

V.TRWF = 7.5 

V.TRWR = 7.5 

V.HF = 0.225 

V.HR = -0.117 

V.HCG = 2.92 

V.KTSF = 501340 

V.KTSR = 1193300 

V.KRASF = 120000 

V.KRADPF = 3000 % 7000 

V.KRADCFF = 0 

V.KRADCFDF = 0 

V.KRASR = 120000 

V.KRADPR = 5000 % 7000 

V.KRADCFR = 0 

V.KRADCFDR = 0 

V.HRAF = 1.6 

V.HRAR = 2.56 

V.HS = 3.34 

V.IXUF = 500 

V.IXUR = 1250 

V.XACC = 0 

V.ZACC = 0 

V.KBTF = -57.21 

V.KVB = 1.4 

V.KMB = 1.4 

V.FBPVL = 100 

V.SWW = 100 

V.SWZ = 0.9 

V.KCF = -0.000001 

V.LSO = 0 

V.BRAKPROP1 = -80 

V.BRAKPROP2 = -200 

V.FXLIMIT = 0 

V.DAMPCOMF = 800 

V.DAMPEXTF = 800 

V.DAMPCOMR = 2000 

V.DAMPEXTR = 2000 

V.AIRBRAKES = 1 

V.BRAKLAG1 = 0.31 

V.BRAKLAG2 = 0.35 

V.ANTIBF = 0 

V.ANTIBLIMF = 0 

V.KANTIBF = 0 

V.ANTIBR = 0 

V.ANTIBLIMR = 0 

V.KANTIBR = 0 
 35 

Table C-2. Full Trailer Parameters 

TR.MASS = 1990 

TR.SMASS = 1890 

TR.UMASSF = 50 

TR.UMASSR = 50 

TR.VLENA = -15 

TR.VLENB = 19 

TR.IXS = 18200 

TR.IYS = 317200 

TR.IXZ = 0 

TR.IZZ = 320000 

TR.KSCF = 0 

TR.KSCB = 0 

TR.DLADV = 0 

TR.DNADV = 0 

TR.DYADV = 0 

TR.DENSITY = 0 

TR.REFAREA = 0 

TR.CDX = 0 

TR.AEROVEL = 0 

TR.KSF = 215840 

TR.KSDF = 864 

TR.KSR = 208000 

TR.KSDR = 864 

TR.TRWF = 7.5 

TR.TRWR = 7.5 

TR.HCG =7.1 

TR.KTSF = 2568000 

TR.KTSR = 2187000 

TR.KRASF = 120000 

TR.KRADPF = 7000 

TR.KRADCFF = 0 

TR.KRADCFDF = 0 

TR.KRASR = 120000 

TR.KRADPR = 7000 

TR.KRADCFR = 0 

TR.KRADCFDR = 0 

TR.HRAF = 2.4 

TR.HRAR = 2.28 

TR.HS = 7.36 

TR.IXUF = 570 

TR.IXUR = 570 

TR.XACC = 0 

TR.ZACC = 0 

TR.KCF = 0 

TR.LSO = 0 

TR.DAMPCOMF = 2200 %0 

TR.DAMPEXTF = 2200 %0 

TR.DAMPCOMR = 2200 %0 

TR.DAMPEXTR = 2200 %0 

%TR.BRAKPROP1 = 200 

%TR.BRAKPROP2 = 200 

TR.BRAKLAG3 = 0.42 

TR.LEND = 10.5 

TR.LENE = 17 

TR.THH= 3.6 

TR.HITCHSP = 600000 

TR.HITCHSPD = 7000 

TR.KTFIFTH = 1146000 

TR.KFADE = 0.0005 

TR.NDRWHL = 4 

TR.NTRWHL = 2 

TR.ANTIBF = 0 

TR.ANTIBLIMF = 0 

TR.KANTIBF = 0 

TR.ANTIBR = 0 

TR.ANTIBLIMR = 0 

TR.KANTIBR = 0 

TR.SUSPENSIONF = 1 

TR.SUSPENSIONR = 1 

TR.HF = 0.035 

TR.HR = 0.169 

TR.LF = 1 

TR.LR = 1 

TR.KSAF = 0 

TR.KSAR = 0 

TR.BF = 0 

TR.BR = 0 

TR.CF = 0 

TR.CR = 0 

TR.DF = 0 

TR.DR = 0 

TR.EF = 0 

TR.ER = 0 

TR.KSLF = 0 

TR.KSLR = 0 

TR.LSAF = 1 

TR.LSAR = 1 

TR.KSADF = 0 

TR.KSADR = 0 

TR.KSAD2F = 0 

TR.KSAD2R = 0 

TR.KBSCF = 600000 

TR.HBSCF = 0.2 

TR.SBSCF = 1E+20 

TR.KBSEF = 600000 

TR.HBSEF = 0.2 

TR.SBSEF = 1E+20 

TR.KBSCR = 600000 

TR.HBSCR = 0.2 

TR.SBSCR = 1E+20 

TR.KBSER = 600000 

TR.HBSER = 0.2 

TR.SBSER = 1E+20 
 36 

Table C-3. Partial Trailer Parameters 

TR.MASS = 1400 

TR.SMASS = 1300 

TR.UMASSF = 50 

TR.UMASSR = 50 

TR.VLENA = -15 

TR.VLENB = 19 

TR.IXS = 12460 

TR.IYS = 217160 

TR.IXZ = 0 

TR.IZZ = 218000 

TR.KSCF = 0 

TR.KSCB = 0 

TR.DLADV = 0 

TR.DNADV = 0 

TR.DYADV = 0 

TR.DENSITY = 0 

TR.REFAREA = 0 

TR.CDX = 0 

TR.AEROVEL = 0 

TR.KSF = 215840 

TR.KSDF = 864 

TR.KSR = 208000 

TR.KSDR = 864 

TR.TRWF = 7.5 

TR.TRWR = 7.5 

TR.HCG = 5.7 

TR.KTSF = 2568000 

TR.KTSR = 2187000 

TR.KRASF = 120000 

TR.KRADPF = 7000 

TR.KRADCFF = 0 

TR.KRADCFDF = 0 

TR.KRASR = 120000 

TR.KRADPR = 7000 

TR.KRADCFR = 0 

TR.KRADCFDR = 0 

TR.HRAF = 2.4 

TR.HRAR = 2.28 

TR.HS = 6.1 

TR.IXUF = 570 

TR.IXUR = 570 

TR.XACC = 0 

TR.ZACC = 0 

TR.KCF = 0 

TR.LSO = 0 

TR.DAMPCOMF = 2200 %0 

TR.DAMPEXTF = 2200 %0 

TR.DAMPCOMR = 2200 %0 

TR.DAMPEXTR = 2200 %0 

%TR.BRAKPROP1 = 200 

%TR.BRAKPROP2 = 200 

TR.BRAKLAG3 = 0.42 

TR.LEND = 10.5 

TR.LENE = 17 

TR.THH= 3.6 

TR.HITCHSP = 600000 

TR.HITCHSPD = 7000 

TR.KTFIFTH = 1146000 

TR.KFADE = 0.0005 

TR.NDRWHL = 4 

TR.NTRWHL = 2 

TR.ANTIBF = 0 

TR.ANTIBLIMF = 0 

TR.KANTIBF = 0 

TR.ANTIBR = 0 

TR.ANTIBLIMR = 0 

TR.KANTIBR = 0 

TR.SUSPENSIONF = 1 

TR.SUSPENSIONR = 1 

TR.HF = 0.035 

TR.HR = 0.169 

TR.LF = 1 

TR.LR = 1 

TR.KSAF = 0 

TR.KSAR = 0 

TR.BF = 0 

TR.BR = 0 

TR.CF = 0 

TR.CR = 0 

TR.DF = 0 

TR.DR = 0 

TR.EF = 0 

TR.ER = 0 

TR.KSLF = 0 

TR.KSLR = 0 

TR.LSAF = 1 

TR.LSAR = 1 

TR.KSADF = 0 

TR.KSADR = 0 

TR.KSAD2F = 0 

TR.KSAD2R = 0 

TR.KBSCF = 600000 

TR.HBSCF = 0.2 

TR.SBSCF = 1E+20 

TR.KBSEF = 600000 

TR.HBSEF = 0.2 

TR.SBSEF = 1E+20 

TR.KBSCR = 600000 

TR.HBSCR = 0.2 

TR.SBSCR = 1E+20 

TR.KBSER = 600000 

TR.HBSER = 0.2 

TR.SBSER = 1E+20 
 37 

Table C-4. Table of Parameters, their Units and Definition 

Data Parameter Units Definition

V.VLENA ft X distance from ms c.g. to front axle 

V.REFAREA ft2 Frontal area of vehicle, used for longitudinal drag 

V.VLENB ft X distance from ms c.g. to rear axle 

V.BF, V.BR 1/ft First order coefficient for change in wheel steer 

angle with suspension deflection 

V.CF, V.CR 1/ft2 Second order coefficient for wheel steer with 

suspension deflection 

V.CDX Longitudinal drag coefficient 

V.DF,V. DR 1/ft First order coefficient for change in wheel 

camber angle, with suspension deflection 

V.EF, V.ER 1/ft2 Second order coefficient for wheel camber angle 

with suspension deflection 

V.HF, V.HR ft li times slope of trailing link in trailing arm 

suspension 

V.HCG ft c.g. height of total mass 

V.HRAF, V.HRAR ft Height of roll axis above ground for solid axle 

suspension 

V.HS ft ms c.g. height above ground 

V.IXS lb-ft-sec2 Moment of inertia for sprung mass in roll 

V.IXZ lb-ft-sec2 Cross product of inertia for sprung mass about 

x-z axis 

V.IXUF, V.IXUR lb-ft-sec2 Moment of inertia for unsprung mass about 

X axis 

V.IYS lb-ft-sec2 Moment of inertia for sprung mass about y axis 

V.IZZ lb-ft-sec2 Moment of inertia for entire mass about z axis 

V.KACK ft/ft Ackerman steer coefficient 

V.KCF rad/sec Lateral force steering compliance for suspension 

and steer linkage 

V.KRADPF, V.KRADPR lb-sec/ft Damping rate at compliant pin joint between 

ms and mu

V.KRASF, V.KRASR lbs/ft Lateral spring rate at compliant pin joint between 

ms and mu

V.KSAF, V.KSAR = 1.0 for solid axle, = 0.0 for independent 

suspension 

V.KSADF, V.KSADR ft/ft Anti dive coefficient, or slope in side view of an 

equivalent single suspension arm 

V.KSAD2F, V.KSAD2R ft/ft Special case for ksadi when there is positive fx

with independent suspension 

V.KSF, V.KSR lbs/ft Suspension spring rate equivalent at each wheel 

V.KSCF, V.KSCB rad-lbs/ft Steering compliance for steering gear 

V.KSDF, V.KSDR lbs-sec/ft Suspension damping rate equivalent at each 

wheel 
 38 

Data Parameter Units Definition

V.KSLF, V.KLSR ft/ft Lateral slope of an equivalent single suspension 

arm, at curb load 

V.KSTR rad/rad Overall steering ratio 

V.KTSF, V.KTSR ft-lbs/rad Auxiliary torsional roll stiffness per axle, 

(normally negative) 

V.LF, V.LR ft Length of trailing link, in a trailing arm 

suspension 

V.LSAF, V.LSAR ft Length of the kslj arm 

V.LSO ft 

Lateral steering axis offset from king pin to tire 

patch center (positive if tire c.l. is outside king pin 

axis) 

V.MASS slugs Total vehicle mass 

V.SMASS slugs Sprung mass 

V.UMASSF, V.UMASSR slugs Front, or rear, unsprung mass 

V.TRWF, V.TRWR ft Track width 

V.SWW rad/rad Natural frequency for second order steering 

system lag 

V.SWZ Damping ratio for steering system lag 

V.DLADV ft-lbs/ft/sec Aerodynamic roll moment coefficient 

V.DNADV ft-lbs/ft/sec Aerodynamic yaw moment coefficient 

V.DYADV lbs/ft/sec Aerodynamic lateral force coefficient 

V. DENSITY lbs/ft3 Air density 

V. AEROVEL ft/sec Aerodynamic reference speed 

V. XACC ft Distance of accelerometer ahead of sprung mass 

c.g. 

V. ZACC ft Distance of accelerometer above vehicle roll axis 

V.KBTF ft-lbs/psi Front brake effectiveness 

V.KVB psi/lbs Brake gain in vacuum boost range 

V.KMB psi/lbs Brake gain in manual range 

V.FBPVL lbs Pedal force where vacuum boost runs out 

V.BRAKPROP1 lbs/lbs, or 

ft-lbs/psi 

Hydraulic: initial f/r brake force slope, air-front 

axle brake effectiveness 

V.BRAKPROP2 lbs/lbs, or 

ft-lbs/psi 

Hydraulic: final f/r brake force slope, air-drive 

and trailer axle brake effectiveness 

V.FXLIMIT lbs 

Hydraulic: front brake force at knee in rear vs. 

front brake force curve (entered as a negative 

number) 

V. DAMPCOMF lbs-sec/ft Front shock compression damping 

V. DAMPEXTF lbs-sec/ft Front shock rebound or extension damping 

V. DAMPCOMR lbs-sec/ft Fear shock compression damping 

V. DAMPEXTR lbs-sec/ft Fear shock rebound or extension damping 

V.AIRBRAKES 0 or 1 Air brake model flag: 0 - off, 1 - on 

V.BRAKLAG1 sec Front axle brake force time constant 
 39 

Data Parameter Units Definition

V.BRAKLAG2 sec Drive axle brake force time constant 

V.BRAKLAG3 sec Trailer axle brake force time constant 

V.ANTIBF 0 or 1 Front axle anti-lock brake flag: 0 - off, 1 - on 

V. ANTIBLIMF - Longitudinal slip ratio limit where the anti-lock 

braking routine for the front turns on and off 

V. KANTIBF ft-lbs/s Anti-lock braking gain for front the brakes 

V.ANTIBR 0 or 1 Rear axle anti-lock brake flag: 0 - off, 1 - on 

V. ANTIBLIMR - Longitudinal slip ratio limit where the anti-lock 

braking routine for the rear turns on and off 

V. KANTIBR ft-lbs/s Anti-lock braking gain for rear the brakes 

TR. LEND ft Distance from vehicle sprung mass c.g. to hitch 

TR. LENE ft Distance from trailer sprung mass c.g. to hitch 

TR.THH ft Trailer hitch height above ground 

TR. HITCHSP lbs/ft Hitch deflection spring stiffness 

TR. HITCHSPD lbs-sec/ft Hitch deflection damping 

TR.KTFIFTH ft-lbs/rad Hitch torsional stiffness 

TR.KFADE %/°f Brake temperature fade parameter 

TR.NDRWHL # Number of tires at each end of drive axle 

TR.TDRWHL # Number of tires at each end of trailer axle 

V.SUSPENSIONF 0 or 1 Front suspension type: 0 - solid axle, 

1 - independent 

V.SUSPENSIONR 0 or 1 Rear suspension type: 0 - solid axle, 

1 - independent 

V.KBSCj lb/ft Compression bump stop stiffness 

V.HBSCj ft Compression bump stop contact point 

V.SBSCj - Compression bump stop transition term 

V.KBSEj lb/ft Extension bump stop stiffness 

V.HBSEj ft Extension bump stop contact point 

V.SBSEj - Extension bump stop transition term 

TIRE(#).TWIDTH ft Tire contact patch width 

TIRE(#).KA0 lbs/rad Cornering stiffness vs. load constant term 

TIRE(#).KA1 1/rad Cornering stiffness vs. load linear term 

TIRE(#).KA2 lbs Cornering stiffness vs. load squared term 

TIRE(#).KA3 1/rad Camber stiffness vs. load linear term 

TIRE(#).KA4 lbs Camber stiffness vs. load squared term 

TIRE(#).KA − Contact patch elongation with fx 

TIRE(#).KX − Change in cornering stiffness with fx 

TIRE(#).KMUY − Decay in lateral friction with increasing slip angle 

TIRE(#).TPRES psi Tire inflation pressure 

TIRE(#).KB1Y 1/lbs Peak lateral friction vs. load linear term 

TIRE(#).KB3Y − Peak lateral friction vs. load constant term 
 40 

Data Parameter Units Definition

TIRE(#).KB4Y 1/lbs2 Peak lateral friction vs. load squared term 

TIRE(#).KGAMMA − Falloff of camber thrust at high slip 

TIRE(#).CSFZ − Normalized longitudinal tire force stiffness 

TIRE(#).MUNOMY − Lateral friction of vehicle test surface 

TIRE(#).MUNOMX − Longitudinal friction of vehicle test surface 

TIRE(#).FZTRL lbs Tire design load 

TIRE(#).KK1 ft/lbs Aligning torque stiffness vs. load 

TIRE(#).C1 − Shaping coefficient, c1, for force saturation 

function (-) 

TIRE(#).C2 − Shaping coefficient, c2, for force saturation 

function (-) 

TIRE(#).C3 − Shaping coefficient, c3, for force saturation 

function (-) 

TIRE(#).C4 − Shaping coefficient, c4, for force saturation 

function (-) 

TIRE(#).C5 − Shaping coefficient, c5, for force saturation 

function (-) 

TIRE(#).G1 − Aligning moment shaping parameter, g1 

TIRE(#).G2 − Aligning moment shaping parameter, g2 

TIRE(#).TLONGLAG sec Longitudinal slip ratio time constant 

TIRE(#).PLYSTEER rad Slip angle offset for zero lateral tire force 

TIRE(#).KB1X 1/lbs Peak longitudinal friction vs. load linear term 

TIRE(#).KB3X - Peak longitudinal friction vs. load constant term 

TIRE(#).KB4X 1/lbs2 Peak longitudinal friction vs. load squared term 

TIRE(#).KMUX − Decay in longitudinal friction with increasing slip 

TIRE(#).DRAGC − Rolling drag coefficient 

TIRE(#).BRAKMULT − Brake torque multiplier 

TIRE(#).STIFFNESS lbs/ft Vertical spring rate of tire 

TIRE(#).DAMPING lbs-sec/ft Vertical damping rate of tire 

TIRE(#).KTL ft Tire lag, expressed in rolling distance 

TIRE(#).KLT ft/lb Lateral compliance rate, of tire, wheel, and 

suspension, per tire 

TIRE(#).RR ft Effective wheel/tire radius, and same as c.g. 

height of mui

DRT.KDC − Center differential gear ratio 

DRT.KDF − Front differential gear ratio 

DRT.KDB − Rear differential gear ratio 

DRT. KCP Center viscous coupling pressure coefficient 

DRT. KCPF Front viscous coupling pressure coefficient 
 41 

Data Parameter Units Definition

DRT. KCPB Rear viscous coupling pressure coefficient 

DRT.KRF - Front torque split differential coefficient 

DRT.KRB - Rear torque split differential coefficient 

DRT.KEK=1 TO 6 - Coefficients for the engine torque curve 

DRT.KTC0 Torque converter coefficient 

DRT.SR0 - Torque converter stall ratio 

DRT.ENGINEI ft-lbs-sec2 Engine rotary inertia 

DRT. TRANSMISSIONI ft-lbs-sec2 Transmission rotary inertia 

DRT.SHIFTTIME sec Time interval for transmission gear shift 

DRT.SPEEDK1 Proportional automatic speed control gain 

DRT.SPEEDK2 Integral automatic speed control gain 

DRT.IDLE rad/sec Engine idle speed 

DRT.DIFFTYPE - Center differential type, choices: 1 - limited slip 

differential, 2 - locked differential 

DRT.DG(K), K=1 TO 10 - 

If the center differential is locked, then dg(1) is 

the drive shaft spring stiffness in ft-lbs-sec^2, 

and dg(2) is the drive shaft damping in ft-lbssec/rad otherwise all are zero 

DRT. TRANSMISSION 0 or 1 0 - Automatic transmission, 1 - Manual 

transmission 

DRT.NUMGEAR - Number of transmission gear ranges (max=20) 

DRT. DOWNSHIFT rad/sec Downshift threshold 

DRT.KGR(K), K=-1 TO 20 - Gear ratios (-1 is reverse) 

DRT.KT1(K), K=1 TO 20 rad/sec Minimum upshift speed from gear k to k+1 

DRT.KT2(K), K=1 TO 20 rad/sec Maximum minus minimum upshift speed k to k+1 

DRT.GEARBYTE(K), K=-1 TO 

20

0 to 255 Byte value of input port used to read current gear 

number 

DRI.TAUA sec The driver's look ahead distance reaction time 

delay 

DRI.TAUR sec The motion feedback time delay 

DRI.KY 1/(ft-sec2) Trim loop gain 

DRI.KR - Motion feedback gain (yaw rate feedback gain) 

DRI.TL sec Driver curvature error lead compensation term 

DRI.KPSI ft/sec Steering loop yaw rate command gain 

DRI.ZN - The damping ratio of the driver's neuromuscular 

dynamics 
 42 

Data Parameter Units Definition

DRI.WN rad/sec The frequency of the driver's neuromuscular 

dynamics 

DRI.KA 1/sec The driver's look ahead distance constant 

(xa = ka*u) 

DRI.KBDSW - Beta to steering wheel compensation gain 

DRI.THROTTLEMAX - Maximum throttle input 

DRI. KBDDSW sec Beta rate to steering wheel compensation gain 

DRI.FBKAY Collision avoidance feedback loop gain 

DRI.KYDOT sec Lane position rate feedback gain 

DRI.KSTABF rad/ft/sec2 Vehicle's stability factor 

DRI.AYD ft/sec2 3d terrain desired cornering ay 

DRI.SPEEDLIMIT ft/sec 3d terrain speed limit 

DRI.KCPRIME 3d terrain trim integrator gain 

DRI.KCVELM 3d terrain proportional throttle gain multiplied by 

mass 

DRI.KSFF 3d terrain steering feed forward gain 

DRI.TAUB sec 3d terrain braking time delay 

DRI.KFBP lbs/throttle 3d terrain braking gain 

DRI.KAS sec 3d terrain driver steering look ahead time 

DRI.KAB sec 3d terrain driver speed control look ahead time 

DRI.YC ft 3d terrain commanded lane position 

NL.SMI - Wheel spin mode integration rate multiplier 

NL.IYW lb ft sec2 Wheel inertia about spin axis 

NL.DSWMAX rad Maximum value the steering wheel may be 

turned in either direction 

NL. BRAKTMAX lbs The maximum limiting brake pedal force 

NL.SIUNITS 0 or 1 Flag for plotting and saving data in si units: 

0 - u.s., 1 - si 

NL.SAVERATE Hz Output data save rate 

NL.ROLLOVER rad Vehicle roll angle where simulation stops 

NL.DISTPLOT 0 or 1 Change plotting and saving data from time base 

to distance based: 0 - time, 1 - distance 

NLSAVEtoDISK 0 or 1 

Change variable storage from RAM (0) to DISK 

(1). Use disk for long runs to avoid using up 

memory 

NL.TERLAGDIST ft Distance used for first order terrain height lag 
For more information on the Federal 

Motor Carrier Safety Administration, 

check out our website at www.fmcsa.dot.gov

Report No. FMCSA-MCRR-06-006