A great number of accident injury cases involve the occupants of vehicles involved in low-speed (5-10 mph) impacts. Generally, the claimants are in a front vehicle which has been hit from behind by the rear vehicle. Claims are often of headaches, neck injuries, or back injuries. In many of these accidents there is very little visible damage to either car; and it is, therefore, difficult to assess the magnitude of the forces experienced by the passengers or the likelihood of serious injury. Because of this, testing has been done both on human subjects and on crash dummies in low speed impacts to quantify the effects of low-speed impacts.
The details of any individual collision would depend on the type and weight of vehicles, the type of bumper, the speed of impact, the types of seats, and the size and weights of passengers. However, all low-speed rearend impacts have the same qualitative dynamics. First, what matters is the relative velocity between the two vehicles. Thus, it does not matter whether the front vehicle backs into the rear vehicle or the rear vehicle runs into the front vehicle, the results are the same. Further, it is of little consequence whether or not the stationary car has the brakes applied.For the sake of explanation, let us assume that the rear car has impacted the front car at a speed less than 10 mph. At the moment of impact, part of the forward momentum of the rear car is transferred to the front car. At a very low speed (less than 5 mph) with little structural deformation, almost all of the momentum is transferred. At speeds above 10 mph, enough permanent deformation occurs that only about one-half of the momentum is transferred. (The other half is expended in the structural deformation process). In any event, the result is a rapid acceleration of the front car within a very short time (on the order of 50-100 msec). This acceleration of the car pushes the seat back of passengers in the forward car into their backs accelerating them forward as well. However, since the head is not usually resting against anything, it tends to remain stationary for longer than the lower body. This has the tendency to make the head initially tilt backwards with respect to the torso. It takes on the order of 200 msec (0.2 sec) for full backward motion, then the head is propelled forward as it catches the rest of the body. This can be quite a rapid forward acceleration. However, the head is propelled only slightly ahead of its original position and then returns back to its normal, vertical location. There is very little forward motion of the body or knees. (See Figure 1)
In contrast, the passengers in the rear vehicle (See Figure 2) are in a reference frame that has been rapidly slowed or stopped. Thus, they feel their bodies being thrown forward against the seat belts and shoulder restraints. When full belt restraint is achieved, the head travels further forward and then is jerked back to the neutral position. It is usually the passengers in the forward vehicle that complain of injuries.
Thus, most tests have concentrated on the motions of passengers in the front vehicle. Naturally, the amount of rearward neck motion is limited by the presence of head restraints. Nevertheless, integral restraints and adjustable head restraints have only reduced whiplash injuries by 28% and 17%, respectively. Furthermore, most tests show little effect of restraints on the major dynamics.ANALYSIS OF DATA
Although data have been gathered under a variety of conditions, most tests fall within certain general, quantitative limits that can help to determine the extent of motions that might be expected in low-speed rear end impacts. In tests at relative velocities of less than 2 mph, we find vehicle accelerations of about .75 g's (75% of the force of gravity) and head accelerations of less than 1.5 g's. The resultant angular head rotations (backwards) are less than 10 degrees. In the range of relative speeds of 3.0 to 4.0 mph, head accelerations increase to about 2.5 to 3.0 g's and head motions reach 20 to 30 degrees. At these speeds, no test subject has reported any pain or injury.
At 5 mph impact, we move into the next level of collisions. Usually, significant vehicle deformations are seen, depending on the details of the impact point. For the occupants of the forward vehicle, head accelerations increase to 6 g's, and backward head rotations reach 45 to 50 degrees. This is roughly the onset of temporary mild neck discomfort due to strain, but healthy subjects report no pain or lasting discomfort from these impacts after they have left the vehicle. On the other hand, some individuals with previous neck or back injuries who are subjected to 5 mph impacts report headaches that last for several minutes or neck stiffness that lasts into the following morning. Still, however, no longer-lasting symptoms have been reported for a period of over a year.In the range of impact speeds from 5 to 10 mph, accelerations increase from 6 g's to 12 g's and head rotations increase from 45 degrees to 70 degrees. Seventy degrees is about the limit of human tolerance and is approaching the limit at which injuries could be expected. Participants in 10 mph tests report headaches and neck discomfort that last from a few hours to several days. Thus, one would expect the possibility of longer-lasting injury at higher speeds, although well-restrained individuals have withstood much higher g's.SUMMARY AND CONCLUSIONS
Impact speeds of less than 2 mph leave no test subject with lasting symptoms. The accelerations and forces are about the same as would be expected in normal vehicle stopping. In the range of 3 to 4 mph, forces are typical of a mild amusement park ride, and no test subjects have reported any lasting effects. At 5 mph, we reach the lower edge of where after-effects can be felt. Accelerations are typical of those felt jumping off a step or "plopping" into a hard chair. In the range from 5 mph to 10 mph (for which vehicle damage is possible), some temporary headache and neck discomfort is reported for hours or days, and persons with previous neck or back injuries feel the effects for a longer period after the collision than do healthy subjects. Nevertheless, all effects have disappeared after this time with no long-term results. For impact above 10 mph, injury is certainly possible but not always necessary, and head restraints can be a mitigating factor.
ABOUT THE AUTHOR
FORCON consultant David A. Peters received his B.S. and M.S. in Applied Mechanics from Washington University and his Ph.D. in Aeronautics and Astronautics from Stanford University. He is currently a Professor of Mechanical Engineering and Director of the Center for Computational Mechanics at Washington University and has been a FORCON consultant since 1989 when he was a Professor at Georgia Tech.Dr. Peters has extensive experience as a forensic consultant and expert witness and has authored over 100 publications in areas of vibration, dynamics, structures, stresses and aerodynamics. His consulting/Expert witness experience has been associated with dynamics of vehicles including rail cars, amusement park rides, aircraft and helicopter dynamics, seat failures, shoe friction, exercise equipment, lawn mowers, and other mechanical devices. He is a registered Professional Engineer in Georgia and Missouri.Dr. Peters also conducts investigations of low speed impacts wherein he determines the relative velocity between the vehicles at impact and then provides an assessment of the liklihood of injury using data contained in the studies he references in the above article.
