There are two common scenarios that lead to in-line multi-vehicle rear-end accidents. The first scenario involves a small number of moving vehicles approaching a line of stopped vehicles (possibly at a red light). The second scenario involves a number of vehicles cruising with a relatively small following distance (headway). One or two of the vehicles apply brakes because of some disturbance and the resulting accident can involve many more vehicles. For either scenario, some vehicles are involved in multiple impacts and physical evidence with which to reconstruct the sequence of impacts is scant.
The first part of the paper reviews analytical methods. Methods published in the past include repeated use of two-vehicle impact relations, and a “coupling” routine that assumes that there is no elastic rebound. Then two unpublished methods are introduced. One method involves applying a newly derived closed-form formula for two vehicles that initially were cruising at the same speed. The formula calculates closing speed during braking given: the following distance, two deceleration rates, and the time lag in braking. The second unpublished method is a numerical initial-value computer program that accounts for vehicle-road friction, inelastic rebound, and repeated in-line impacts.
The second part of the paper presents numerical results. A series of calculations, involving one bullet vehicle and two target vehicles, is used to illustrate the sensitivity of the calculated impacts to the specified impact parameters (such as restitution coefficient). If there is a large number of vehicles stopped at a traffic light, and there is one bullet vehicle, the total number of vehicles involved in the collision is calculated to be: five for a bullet speed of 41 ft/sec (28 mph), and six for a bullet speed of 51 or 61 ft/sec (35 or 41 mph).
A series of four-vehicle calculations is then performed and analyzed to evaluate whether an accident at a red light involved one or two bullet vehicles. It is found that crush patterns can be used to help identify the number of bullet vehicles.
Finally, based on all the calculated results, the four different analytical methods are evaluated.