Last month we discussed a case where a 2000 Camry slammed head-on into a concrete retaining wall. Assuming a simple linear plastic spring model, the crush of the car was used to estimate the speed of impact (V) to be 38 mph, using energy principles and crash test data.
What happened to the occupants is usually of more significance than what happened to the car(s). Analyzing the dynamics of occupants during impact may shed light on causal factors, and explain injuries. In cases where fraud may be suspected in connection with claimed injuries, knowledge of occupant dynamics can be enlightening.
Newton's First Law is important in analyzing occupant dynamics. This basically says that an occupant sitting at rest in a parked car will tend to remain stationary in space even though the car is struck and begins to move. As the car moves, it exerts unbalanced forces on the occupants, causing them to move. In a car in motion at 60 mph, quietly seated occupants are also moving at 60 mph. In a collision, the occupants tend to keep going at 60 mph. If the car stopped instantly, traveling at 60 mph inside a car could ruin your whole day. If a car is struck from the rear and accelerated forward, unconstrained occupants would be accelerated toward the rear of the car until impacting car structures accelerated them forward. Since occupants are in the car, it is their motion relative to the car that is important. A common misconception is impact throws occupants forward into the steering wheel, dashboard, and windshield. In actuality, injuries from hitting these structures are secondary due to rebound from the initial motion toward the rear.
Injuries result from several mechanisms inside the car including body parts hitting the steering wheel, windshield, doors, etc. Acceleration of unconstrained parts of the body relative to constrained parts can also cause injury, as in whiplash. To minimize injury, it is necessary to minimize the acceleration experienced by the car, and thus the occupants.
Using the simple model for crush, and ignoring bumper effects, the relationship between the impact force (F) and the crush depth (D) is given by:
F = KD
K is the stiffness coefficient for the vehicle, usually determined from crash test data. The stiffness (related) coefficient in the velocity equation used last month is k = (K/m)½. Equating the kinetic energy dissipated during crush to the work required to produce the crush, we find the relationship:
D = (m/K)½V
F = KD = (mK)½V = ma
Where "a" is the acceleration, and m is the mass, giving:
a = (K/m)½V
If K increases, "a" and F increase, and D decreases. A stronger vehicle reduces the crush, but increases the potential for injury due to acceleration of the occupants. Some cars are designed to be "softer" to reduce acceleration during collision. As crush increases, the vehicle becomes stiffer as hard structures like the engine, transmission, axles, etc. become involved. Some designs provide for these structures to shear off their mounts and slide under the car body to reduce stiffness. It is also important to ensure that there is minimum intrusion into the passenger compartment. This can be accomplished by strengthening that structure.
For the Camry, we calculate a peak acceleration of 46 g's. Since the impact is on the front, the occupant is accelerated toward the front of the car. For impact with the car to accelerate a 200-lb man at 46 g's requires a force of 9,194 lbs, ignoring momentum considerations. As in sky diving, it's not the acceleration that gets you, it's the sudden stop.