AC 2011-1919: RECONSTRUCTION OF AN ACTUAL VEHICLE ROLLOVERAS A SPECIAL PROJECT IN AN UNDERGRADUATE DYNAMICS COURSE

Blake M. Ashby, Grand Valley State University

Blake M. Ashby is an Assistant Professor of Mechanical Engineering in the School of Engineering atGrand Valley State University. His research and teaching interests include the areas of dynamics, kine-matics, solid mechanics, musculoskeletal biomechanics, injury biomechanics, and accident reconstruc-tion. Prior to joining to Grand Valley State, he worked for several years as a consulting engineer withWoolley Engineering Research Corporation and Exponent Failure Analysis Associates. He received aB.S. degree in Mechanical Engineering from Utah State University and M.S. and Ph.D. degrees in Me-chanical Engineering from Stanford University. He is a registered Professional Engineer.

Alan F. Asay, Woolley Engineering Research Corp.

Over 25 years of engineering experience in the field of accident reconstruction consisting of consulting,testing, and research. Since 1992 has been employed at Woolley Engineering Research Corp. as a leadconsultant and Professional Mechanical Engineer. Received a B.S. and M.S. from Brigham Young Uni-versity in 1990 and 1992 respectively. Has been a practicing Professional Mechanical Engineer since1994. Served as an active member of SAE, ASME, and the American Society of Professional Engineers.Has both authored and/or co-authored 6 SAE publications.

c©American Society for Engineering Education, 2011

Reconstruction of an Actual Vehicle Rollover as a Special Project

in an Undergraduate Dynamics Course

Abstract

The reconstruction of a vehicle rollover was assigned as a special group project in an

undergraduate course in dynamics at Grand Valley State University. The students were provided

with a diagram documenting the path of an actual vehicle rollover. Using the principles learned

in the dynamics course, the students were tasked with determining the translational velocity of

the vehicle throughout the event, including the pre-trip, trip, and tumbling phases. The project

also required the students to calculate the yaw rate prior to trip and the roll rate during the

tumbling phase of the event. With the translational and rotational velocities along with the

relevant geometry of the vehicle, the students were able to determine the trajectories of a

hypothetical occupant ejected from the vehicle at different points in time throughout the rollover

and estimate the locations where the occupants would come to rest. The data for this rollover

came from a test conducted on a rural highway by Woolley Engineering Research Corporation.

A 1994 Nissan Pathfinder was towed to highway speed before being released, at which point an

automated steering controller steered the vehicle through a series of maneuvers that resulted in

rollover. The test was documented with on-board high-speed instrumentation and two off-board

high-speed video cameras. This instrumented test allowed for the direct comparison of the

students’ reconstructions of the rollover event with what actually occurred. This course project

gave the students the opportunity to demonstrate that the principles taught in their undergraduate

dynamics course can be used to effectively and accurately analyze a real-world event. In a

student survey conducted at the end of the course, 95% of the students reported that they felt that

completing this project enhanced their understanding of the principles of kinematics and

dynamics that were taught in the class.

Overview

One of the key challenges in undergraduate engineering education is helping students understand

how the theoretical principles they learn in their coursework can be applied to solving real-world

engineering problems. This can be especially challenging in a core mechanical engineering

course like dynamics. As the students work through problem set after problem set, they can find

it difficult to see how solving the contrived, simplified problems from the book actually relates to

analyzing dynamics in the “real world.” To help the students begin to see how dynamics is

applied by practicing engineers, a special group project was assigned to two sections of an

undergraduate dynamics course taught at Grand Valley State University. In groups of two or

three, the students were given the opportunity to demonstrate that the principles taught in this

dynamics course can be used to effectively and accurately analyze a real-world event such as an

actual on-road vehicle rollover.

Figure 1 – Scene diagram of entire event

from just after the vehicle starts to turn

left (position 28), to trip (position 15), and

to rest (position 0)

Figure 2 – Front view of 1994 Nissan

Pathfinder with relevant cross-sectional

geometry

Table 1 – Vehicle Center of Gravity (CG)

positions and Orientations Throughout

Event

Heading

Roll

number

Position x (ft) y (ft) φ φ φ φ (deg)

0 0.0 0.0 111.3 3.50

1 -1.9 0.7 159.7 3.50

2 -11.1 7.3 -175.2 3.25

3 -18.3 10.1 -161.2 3.00

4 -24.4 12.3 -147.9 2.75

5 -31.2 14.9 -143.7 2.50

6 -39.3 17.6 -140.4 2.25

7 -45.8 19.3 -135.8 2.00

8 -52.2 20.8 -133.2 1.75

9 -59.3 22.4 -115.4 1.50

10 -67.0 23.3 -109.4 1.25

11 -73.9 23.9 -99.0 1.00

12 -79.8 24.1 -93.9 0.75

13 -86.5 24.2 -85.5 0.50

14 -94.1 24.4 -68.5 0.25

15 -109.0 24.5 -50.9 0.00

16 -119.0 25.2 -35.4 0.00

17 -135.2 24.8 -16.7 0.00

18 -153.3 23.0 -7.8 0.00

19 -173.7 19.3 1.6 0.00

20 -194.6 15.2 11.7 0.00

21 -215.3 10.6 19.5 0.00

22 -241.0 5.4 17.0 0.00

23 -264.7 1.6 13.8 0.00

24 -287.7 -0.8 7.0 0.00

25 -310.5 -2.7 3.4 0.00

26 -335.0 -3.8 2.1 0.00

27 -358.9 -3.8 0.3 0.00

28 -385.1 -3.8 0.3 0.00

Vehicle CG

positions

The students were provided a scene diagram that depicts the positions and orientations of the

vehicle throughout the event (see Figure 1). They were also provided the relevant vehicle

geometry (see Figure 2) and the positions and orientations of the vehicle for each position shown

in Figure 1 (tabulated in Table 1). The deliverable for this project was a written report, one per

group.

Test Description

The data for this rollover came from a test conducted with a 1994 Nissan Pathfinder by Woolley

Engineering Research Corporation in August 2009. Prior to conducting the rollover test, non-

essential items and select fluids were removed from the vehicle. The tires were inflated to the

manufacturer recommended pressures. A custom-designed, programmable, pneumatic steering

mechanism was installed in the driver seat and attached to the steering wheel. On-board

instrumentation was added with a high-speed data acquisition system that included one tri-axial

accelerometer pack, three rotation sensors, one string potentiometer, and two independent speed

sensors. The windows, mirrors, turn signals, and headlights were painted colors according to

their locations on the vehicle to aid in identification of post-test debris.

The rollover test was conducted on a remote highway selected because of its rural nature, low

traffic, and well-maintained condition. The Pathfinder was towed by a modified International

10-wheel tractor to the speed selected for this test. When the Pathfinder reached the desired

speed and the predetermined location, it was released. Upon release, high-speed data collection

began and the automated steer-controller was actuated. The basic steer sequence was to turn

sharp left approximately one-quarter turn and then to turn back hard to the right. At that point,

the controller held the steering wheel in a full right turn until the end of the program (8 seconds

after release) when the brakes were finally applied.

Following the test, the physical evidence, including tire marks, debris, landings, and rest position

were photographed and measured for later reference in producing a scale diagram (see Figure 1).

The high-speed data collected was filtered and presented in graphical form for event timing and

correlation analysis. The high-speed video was synchronized with the high-speed data and

utilized in the correlation of specific events throughout the test. More details on the testing

methodology, results, and conclusions can be found in a paper written by Asay and Woolley1.

Assumptions

A vehicle rollover is an extremely chaotic and complex event. A detailed reconstruction of the

vehicle’s three-dimensional translational and rotational kinematics is not practical, even for

practicing engineers with years of experience. Nevertheless, with appropriate simplifications,

valuable information can be learned about the vehicle’s motion throughout the event. For the

purposes of this course project, the students were instructed to make the following simplifying

assumptions: air drag was insignificant, there were no elevation changes of the ground in the

vicinity of this event, the vehicle’s rotation was solely about its longitudinal axis during the

tumbling phase, and the vehicle rolled along the ground during the tumbling phase (i.e., it did not

vault vertically into the air).

Analyses

With the information provided, the students were tasked with completing a series of analyses that

built upon each other:

a) Calculate the translational speed of the vehicle center of mass (vG) throughout the event.

b) Calculate the angular velocity of the vehicle about its longitudinal axis (i.e., roll rate) for

the rollover phase and about a vertical axis (i.e., yaw rate) for the pre-trip and trip phases.

c) Calculate the velocity of the upper door frame of the driver’s door (point P in Figure 2)

relative to the vehicle’s center of mass (point G) (���/�) throughout the rollover phase.

d) Calculate the total velocity of point P (���) throughout the rollover phase.

e) Using the velocity vector calculated in d) as the initial velocity of a potentially ejected

occupant and the height of the ejection point (point P in Figure 2), calculate the

maximum height above the ground that a potentially ejected occupant would reach for

each position from the end of trip to rest.

f) Calculate the horizontal distance that the occupant would travel in the air before

impacting the ground for each position from the end of trip to rest.

g) Taking into account the location of the occupant when ejected, calculate the location of

ground impact for the occupant for each position from the end of trip to rest.

h) Calculate the components of velocity at ground impact for the occupant for each position

from the end of trip to rest.

i) Using the velocities calculated in h), calculate the components of the average force the

ground exerts on a 170 lb occupant during impact for each potential ejection position.

j) Calculate the distance the occupant slides along the ground before coming to rest for each

potential ejection position.

k) Calculate the coordinates of the rest position of the occupant for each position.

l) Calculate the normal acceleration of point P for each position.

m) Calculate the normal force an unrestrained occupant that weighs 170 pounds exerts on the

point P. (Assume all of the occupant’s weight is located at point P).

Example solutions to these analyses are displayed in the Appendix.

Additional Instruction Provided

Vehicle Deceleration During Rolling Phase (Positions 15 to 0): Accident reconstructions

typically are done by starting at the position of rest and moving backwards in time. Knowing

that the translational velocity of the vehicle is zero at rest, the velocity of the center of mass of

the vehicle at previous positions can be calculated if the distance between positions is known and

a constant deceleration rate is assumed. Accident reconstructionists routinely assume a constant

deceleration of the vehicle’s translational speed during the vehicle’s rolling phase. In reality, the

deceleration of the vehicle’s speed is not constant while tumbling. Almost all of the deceleration

occurs in discrete bursts during the ground contacts with virtually no deceleration occurring

during the periods that the vehicle is airborne. However, for any given accident, there is not

enough evidence at the scene or on the vehicle to precisely model the dynamics, so a constant

deceleration model is assumed. Experimental studies over the years by Cooperrider, et al.3,

Orlowski, et al.6, and Leupke, et al.

5 have found average deceleration rates ranging from 0.36 g

to 0.61 g for the rollover phase. For this analysis, the students were instructed to select a

constant deceleration rate and justify their choice based on these three studies.

Deceleration During Pre-Trip Phase (Positions 28 to 17): The deceleration during the pre-trip

phase of the event as the vehicle is yawing is a function of the slip angle of the vehicle. The slip

angle is the angle between the vehicle’s heading (forward longitudinal axis) and its velocity

direction (direction of travel of the center of mass). The deceleration was expressed by a = feg.

The effective drag factor, fe, was estimated with the following relationship2:

�� = � sin + �� cos

where fn is the nominal drag factor between the tires and the road surface, fr is the drag associated

with power train and rolling resistance, and α is the slip angle. Performance tests conducted by

the Utah Highway Patrol on this roadway found the nominal drag factor to be 0.771. For this

analysis, the students assumed a value of 0.1 for fr. During the pre-trip phase, as the vehicle

leaves the roadway, fn and fr would deviate some from these values. However, for the purposes

of this analysis, the students assumed that these values were constant throughout the pre-trip

portion of the event (positions 28 to 17).

Deceleration During Trip Phase (Positions 17 to 15): Just before the vehicle starts to overturn,

the effective drag factor increases significantly as the tires furrow into the ground. In testing by

Cooperrider, et al.3, the drag factor during the trip phase for a soil tripped rollover was about 1.7.

Angular Rates: The relevant angular positions (roll angle and yaw angle) were provided for

positions 0 to 28 (see Table 1). The roll rate and yaw rate were calculated by taking the time

derivatives of the roll angle and yaw angle, respectively. There are many ways to calculate

derivatives of discrete data including finite difference methods, Fourier analysis, polynomial

curve fitting, spline fitting, etc. Most of these numerical methods are beyond the scope of the

course, so for this analysis, the students used finite difference formulas.

Impact of Ejected Occupant and Ground and Sliding Phase: For the analysis of the impact

between the potentially ejected occupant and the ground, the students were instructed to assume

a coefficient of restitution of e = 0.1 for the vertical impact with the ground and assume the time

duration for the impact to be 0.1 sec (actual impact duration is likely shorter than this). A typical

undergraduate dynamics course only covers frictionless impacts, but that is not a very good

assumption for the impact between the occupant and the ground. Therefore, the students were

instructed to model the decrease in the horizontal component of the occupant’s velocity (vh)

during the impact with the following relationship7:

∆�� = −����

where vv is the vertical component of the occupant’s velocity at ground impact and fs is the

sliding drag factor for the occupant. One study cited a value of 0.66 for the sliding drag factor in

testing involving anthropomorphic test devices (ATDs or crash test dummies)4. For the sliding

phase of the occupant’s motion following impact, the students assumed a constant deceleration

of a = fsg.

Interpretation of Results

In addition to completing the series of analyses detailed above, the students were expected to

demonstrate that they could properly interpret the significance of the results by addressing a

series of discussion questions:

• If the ejected occupant had severe blunt force injuries to his or her body, which ejection

location(s) would be more consistent with those injuries?

• If the ejected occupant demonstrated multiple abrasions all over his or her body, which

ejection location(s) would be less consistent with those injuries?

• Which ejection positions had the potential to cause the occupant to be rolled over by the

vehicle following ejection?

• Assuming the occupant was found at coordinates of (30 ft, -30 ft) with respect to the rest

position of the vehicle CG, which ejection location(s) are most likely?

• Assuming the occupant was found at x-y coordinates of (170 ft, 10 ft) with respect to the

rest position of the vehicle CG, which ejection location(s) are most likely?

• Currently, most vehicles use tempered glass for the side windows. It has been suggested

that laminated glass (similar to what is used for front windshields) should be used for side

windows to help prevent ejections in rollovers. Assume that tempered glass side

windows fracture under a normal load of about 400 pounds. Also assume that laminated

glass side windows systems could be designed to double the load needed to cause the

window to be pushed out. How effective would laminated side glass be in preventing

ejection of an unbelted occupant in this rollover?

Student Evaluations

The students were asked to provide feedback on the course project by completing a survey using

a scale from 1 to 5 for their responses to the first 9 statements (1: Strongly disagree, 2: Disagree,

3: Neither agree nor disagree, 4: Agree, 5: Strongly agree). The last two questions were in

relation to group size.

1. The project enhanced my understanding of the principles of kinematics and dynamics that

were taught in this class.

2. The project was interesting and worthwhile.

3. My ability to use computational software to analyze kinematic and dynamic systems was

increased through completing this project.

4. Completing this project increased my interest in the subject matter presented in the

lectures.

5. The amount of work required to complete the project was appropriate.

6. Sufficient instruction was provided to complete the project.

7. I am more confident in my ability to analyze dynamic systems as a result of completing

this project.

8. My ability to work as a member of a team to solve engineering problems increased while

completing the project.

9. I have a greater understanding of how the principles taught in the lectures can be applied

to real-world engineering problems because of this project.

10. How many students were in your group?

11. How many students per group are ideal for a project such as this one?

There were 49 students enrolled in the two sections of dynamics that completed this project.

Based off 43 completed surveys, the numerical average for the responses to the questions on the

survey is shown in Table 2. Also, the percentage of students who agreed or strongly agreed is

listed.

Table 2 – Results of Student Survey

1 2 3 4 5 6 7 8 9 10 11

Average Score 4.3 4.4 3.6 4.3 4.3 4.5 4.1 4.0 4.5 2.8 2.8

% Who Agreed 95.3 93.0 55.8 88.4 95.3 95.3 90.7 83.7 95.3 n/a n/a

Some representative student comments include:

• “I enjoyed the project. I really appreciated the very practical application for what was

learned in the course.”

• “I liked the idea behind the project, enjoyed seeing how dynamics could be applied to

real world ideas.”

• “Very helpful for my understanding of the class.”

• “I liked how this project applied the things we learned in class to a real life situation.

Also, I liked having the project be based on a real experiment so that there were actual

results we could compare our results too (sic).”

• “This project was very interesting and helped to reinforce several concepts learned this

semester.”

• “Well organized. I'm impressed with the various concepts that could be applied in one

project.”

Discussion

The primary objective for assigning this special group project was to enhance the students’

understanding of the principles taught in their dynamics course. While it is difficult to

objectively measure whether or not this was accomplished, the subjective impressions of the

students overwhelmingly indicate that they feel this objective was achieved. In the student

survey, 95.3% reported that completing this project enhanced their understanding of the

principles of kinematics and dynamics that were taught in the class (survey question 1), and

90.7% indicated that they were more confident in their ability to analyze dynamic systems as a

result of completing this project (survey question 7).

Another reason this project was selected was the breadth of principles that were used in the

various analyses. The following subject areas covered in an undergraduate dynamics course

were used in the completion of this project: uniform motion, uniformly accelerated motion,

projectile motion, rigid body rotational kinematics (angular displacement and velocity), rotating

reference frames, friction, Newton’s second law, conservation of energy, principle of impulse

and momentum, impacts, coefficient of restitution, and relative displacement, velocity, and

acceleration in linear and rotational environments.

The project appeared to enhance the students’ ability to properly work as a member of an

engineering team (83.7% of the students agreed that their ability to work as a member of an

engineering team increased while completing the project) (survey question 8). It is interesting to

note the close correlation between the actual number of students per group (2.8 on survey

question 10) and the ideal number of students per group (2.8 on survey question 11). It seems

that a group size of two to three students is appropriate for a project such as the present one.

Another objective of this project was to help the students understand how the theoretical

principles they learn in their coursework can be applied to solve real-world engineering

problems. 95.3% of the student reported that they had a greater understanding of how the

principles taught in the lectures can be applied to real-world engineering problems because of

this project (survey question 9). This course project was good example of how effective

collaboration with practicing engineers in industry can enhance educational outcomes.

Conclusion

The reconstruction of an actual vehicle rollover by two- or three-member student groups served

to enhance the students’ understanding of the principles of kinematics and dynamics taught in an

undergraduate dynamics course. Using the concepts covered in the course, the students

estimated the translational and rotational velocities of the vehicle throughout the event. They

also determined the trajectories of a hypothetical occupant ejected from the vehicle during the

rollover and estimated the locations where the occupant could have come to rest. Through

completing this project, the students showed that the principles taught in their undergraduate

dynamics course can be used to effectively analyze a real-world dynamic event.

Acknowledgments

Special thanks are given to Woolley Engineering Research Corporation for funding and carrying

out this rollover test and allowing the students access to the results of the test for this project.

References

1. Asay, A.F. and Woolley, R.L. (2010) “Rollover Testing of Sport Utility Vehicles (SUVs) on an Actual

Highway,” Society of Automotive Engineers, SAE 2010-01-0521.

2. Brach, R.M. and Brach, R.M. (2005) Vehicle Accident Analysis and Reconstruction Methods, SAE

International, Warrendale, PA.

3. Cooperrider, N., Thomas, T., and Hammoud, S. (1990) “Testing and Analysis of Vehicle Rollover Behavior,”

Society of Automotive Engineers, SAE 900366.

4. Funk, J.R. and Leupke, P.A. (2007) “Trajectory Model of Occupants Ejected in Rollover Crashes,” Society of

Automotive Engineers, SAE 2007-01-0742.

5. Leupke, P.A., Carter, J.W, Henry, K.C., Germane, G.J., and Smith, J.W. (2008) “Rollover Crash Tests on Dirt:

An Examination of Rollover Dynamics,” Society of Automotive Engineers, SAE 2008-01-0156.

6. Orlowski, K.F., Moffatt, E.A., Bundorf, R.T., and Holcomb, M.P. (1989) “Reconstruction of Rollover

Collisions,” Society of Automotive Engineers, SAE 890857.

7. Searle, J.A. and Searle, A. (1983) “The Trajectories of Pedestrians, Motorcycles, Motorcyclists, etc., Following

a Road Accident,” Society of Automotive Engineers, SAE 831622.

Appendix (Results of Analyses)