The Traffic Accident Reconstruction
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Re: Rear end collisions followed by frontal
Bruno Schmidt (SchmidtBF@aol.com)
Sun, 13 Apr 1997 10:18:25 -0400 (EDT)
If a rear-end/front-end collision sequence is NOT independent (ie, if at the time of the second (front-end) collision, the occupant is still moving relative to the vehicle because of the first (rear-end) collision, then the speed with which the occupant strikes the front interior can be much greater than the individual speeds associated with the separate collisions. This is true even if the seat back, etc does not collapse or if the occupant is not really "out of position". It works this way: If the rear-end collision causes a delta-v1 of the target vehicle, then to a rough approximation, the occupant will initially move backwards at delta-v1 relative to the car. Upon pushing against the seat back and the head restraint, the occupant will bounce forward at some speed relative to the car that is a fraction of delta-v1 (due to the elasticity, or coefficient of restitution of the seat back). Say that coeff of restitution is 0.3--then the occupant will bounce forward with a speed of 0
.3 x delta-v1 relative to the car, or a speed 1.3 x delta-v1 relative to the ground (and relative to the stopped car in front of the target vehicle). The target vehicle becomes the bullet car for the second collision. If its speed change is delta-v2 as a result of the second collision, then the occupant will strike the front interior with a relative speed, roughly approximated, of delta-v2 plus 1.3 delta-v1. Thus the speed with which the occupant strikes the interior can be greater than delta-v1, delta-v2, and even delta-v1 plus delta-v2. If the occupant is restrained by a lap/shoulder belt, the forces generated by the belt will be those related to a deceleration associated with the higher relative speed, hence higher acceleration and higher force from the belt than from an isolated front-end collision..
Therefore, if there is a delta-v for each collision of, say, 20 mph, then the delta-v of the occupant from the combined collisions cold be 40 - 50 mph--a drastically more severe situation.
If the collision sequence occurs over a couple of hundred milliseconds and the speed of the middle car between collisions averages, say, 20 mph, then the distance traveled by the middle car between collisions is roughly six feet.
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