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Externally applied unbalanced forces and their corresponding impulses are generally excluded from consideration in regards to the evaluation of the collision phase events for a system comprised of two motor vehicles undergoing collinear impact. This exclusion is generally warranted secondary to the fact that the collision force and its corresponding impulse are dominant during the collision phase. Conceptually, two exclusions exist to this approach. The first is the situation in which significant physical restraints are present to the displacement of one or both collision partners and are of sufficient magnitude as to require inclusion. Generally, this represents the exceptional case and includes, but is not limited to, situations in which one vehicle is snagged, in a non-eccentric manner, by a rigid narrow-width object such as a pole or other similar restraint, prior to the occurrence of the subsequent vehicle-to-vehicle collision under evaluation.

Accident reconstruction typically requires estimating the change of velocity (Delta-V) imparted to vehicles during collision. Estimating Delta-V commonly involves measuring or estimating the deformation of the vehicles involved in a collision. Material coefficients, which relate barrier equivalent velocity (BEV) to deformation for the two vehicles, are then interpolated or extrapolated from barrier crash test data. Finally, the Delta-V for each of the two vehicles is usually calculated using single-degree-of-freedom (SDOF) impact mechanics formulas. This paper presents a derivation of SDOF impact mechanics formulas applicable to one-dimensional vehicle collisions. The governing equations presented are new, more complete and more efficient than previously published efforts. In particular, Newton's third law of physics concerning collision force is proportionally expressed as the product of vehicle weight, crush progression behavior and BEV.

Human volunteer kinematic response to low speed rear-end collisions was investigated. Nominal 16 kph (10 mph) car-to-car impacts were conducted, using human volunteers and anthropomorphic dummies. The human volunteers were both male and female, aged 27 to 58 years, with various degrees of cervical and lumbar spinal degeneration (documented by MRI scan) at the time of the tests. Human volunteer response was monitored and analyzed via accelerometers and high speed film. The impacts resulted in no injury to any of the human volunteers, and no objective changes in the condition of their cervical or lumbar spines. The results indicate a minimum injury tolerance to low speed rear-end impacts for males and females with various degrees of spinal degeneration. Kinematic responses of the head, mandible, upper torso and knees are discussed in light of existing theories regarding injury causation and tolerance.