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Predictions of occupant motion in passenger vehicles undergoing rollovers have been hampered by the uncertainties of the vehicular motion. These uncertainties arise due to a host of factors which may be difficult to quantify, such as trip conditions, vehicle/terrain interaction dynamics and mass eccentricities. In this paper the initial segment of a roll sequence of high angular velocity (greater than 4 radians per second) about a longitudinal axis is examined. The resultant unrestrained motions of the near and far side occupants are studied. To facilitate this analysis a mathematical model has been developed which incorporates dynamic characteristics of the occupant, the vehicle and the terrain surface. The analysis is carried through the first significant vehicle/ground impact following roll initiation. Occupant kinematics are described.

The restitution or rebound that occurs as the final phase of a vehicle-to-vehicle collision is quantified by the coefficient of restitution, which is the ratio of the closing velocity to the post-impact separating velocity of the two colliding vehicles. The coefficient of restitution of medium and high velocity collisions is low, [approximately 0.1] since these collisions are quite inelastic, whereas collisions at extremely low velocities are relatively elastic with the coefficient of restitution theoretically approaching 1.0. However, the actual collision restitution magnitude in the low velocity range has not been adequately established. A series of vehicle-to-vehicle and vehicle-to-barrier collisions resulting in velocity changes in the 2 to 5 miles per hour range was conducted in which vehicles with various bumper configurations [factory standard equipment] were utilized to study the coefficient of restitution at low closing velocities.