Mathematical modeling of rollover accidents
Rollover accidents were studied using epidemiologic data, trajectory analysis, lumped parameter modeling, and occupant simulation techniques. Epidemiologic data were analyzed to determine the critical factors responsible for inducing trauma in rollover crashes. These factors were ejection, restraints, initial roll velocity, and number of rolls. Ejection increased the odds of injury severity, whereas restraints resulted in mitigating trauma. Increase in initial roll velocity resulted in an increase in the distance travelled, the number of rolls, and occupant injuries. The trajectory analysis determined the vehicle speed at each launch, the vehicle launch angle, and the angle and speed of ejection. To determine the forces transmitted to the occupant, a multi-degree-of-freedom system lumped parameter model was developed. The model included the occupant torso, head, neck, restraint and seat. Using representative ranges in the data (such as vehicle weight and head clearance), parametric studies were conducted. Impact velocity was directly related to forces on the occupant. Further, occupant forces reduced with increased superstructure rigidity, increased survival space, and increased restraint stiffness. For the three-dimensional kinematic simulation the Articulated Total Body (ATB) model was used. The occupant was modeled using fifteen segments (the lower torso, center torso, upper torso, neck, head, right upper leg, right lower leg, right foot, left upper leg, left lower leg, left foot, right upper arm, right lower arm, left upper arm, and left lower arm). The automobile was modeled as primary and secondary vehicle. The secondary vehicle segment represented the actual rolled-over vehicle. The secondary vehicle segment simulated the intrusion of the roof into the occupant compartment. Simulation was done to investigate the effects of roof crush, head clearance, and roll velocity on the kinematics of a restrained driver. Occupant motions indicated various dynamic contacts with the vehicle interior. Higher forces were associated with increased accelerations between the occupant's segments (e.g., head) and the vehicle planes (e.g., roof). Increased roof crush increased the transmitted forces to the head-neck region. At any given initial velocity, increased head clearance reduced the forces on the occupant. (Abstract shortened with permission of author.)
Abdullah AbdulKarim Almusallam,
"Mathematical modeling of rollover accidents"
(January 1, 1989).
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