Whiplash

Last week, my wife Shirley and I were in an automobile accident. We suffered no serious injuries, thank you, but the car was totaled and we were sore for several days. After the obligatory reflections on the meaning of life, I began to think critically about the biomechanics of auto accident injuries.

Our car was at a complete stop, and the idiot in the other car hit us from behind. The driver’s side air bag deployed and the impact pushed us off to the right of the road (we hit the car in front of us in the process), while the idiot’s car ended up on the opposite shoulder. It looked a little like this; we were m₂ and the idiot was m₁:

The collision dynamics of our car accident.

The police came and our poor car was carried off on a wrecker to a junk yard. Shirley and I walked home; the accident occurred about a quarter mile from our house.

My neck is still stiff. Presumably I suffered a classic—but not too severe—whiplash. Although Intermediate Physics for Medicine and Biology does not discuss whiplash, it does cover most of the concepts needed to understand it: acceleration, shear forces, torques, and biomechanics. Paul Davidovits describes whiplash briefly in Physics in Biology and Medicine. From the second edition:

5.7  Whiplash Injury

Neck bones are rather delicate and can be fractured by even a moderate force. Fortunately the neck muscles are relatively strong and are capable of absorbing a considerable amount of energy. If, however, the impact is sudden, as in a rear-end collision, the body is accelerated in the forward direction by the back of the seat,  and the unsupported neck is then suddenly yanked back at full speed. Here the muscles do not respond fast enough and all the energy is absorbed by the neck bones, causing the well-known whiplash injury.

You can learn more about the physics of whiplash in the paper “Kinematics of a Head-Neck Model Simulating Whiplash” published in The Physics Teacher (Volume 46, Pages 88–91, 2008).

In a typical rear-end collision, the vehicle accelerates forward when struck and the torso is pushed forward by the seat. The structural response of the cervical spine is dependent upon the acceleration-time pulse applied to the thoracic spine and interaction of the head and spinal components. During the initial phases of the impact, it is obvious that the lower cervical vertebrae move horizontally faster than the upper ones. The shear force is transmitted from the lower cervical vertebrae to the upper ones through soft tissues between adjacent vertebrae one level at a time. This shearing motion contributes to the initial development of an S-shape curvature of the neck (the upper cervical spine undergoes flexion while the lower part undergoes extension), which progresses to a C-shape curvature. At the end of the loading phase, the entire head-neck complex is under the extension mode with a single curvature. This implies the stretching of the anterior and compression of the posterior parts of the cervical spine.

Here are links to videos showing what happens to the upper spine during whiplash:

http://www.injuryresources.com/brain-injury/injury44.html

http://www.injuryresources.com/brain-injury/injury45.html

http://www.injuryresources.com/brain-injury/injury46.html

Injury from whiplash depends on the acceleration. What sort of acceleration did my head undergo? I don’t know the speed of the idiot’s car, but I will guess it was 25 miles per hour, which is equal to about 11 meters per second. Most of the literature I have read suggests that the acceleration resulting from such impacts occurs in about a tenth of a second. Acceleration is change in speed divided by change in time (see Appendix B in IPMB), so (11 m/s)/(0.1 s) = 110 m/s², which is about 11 times the acceleration of gravity, or 11 g. Yikes! Honestly, I don’t know the idiot’s speed. He may have been slowing down before he hit me, but I don’t recall any skidding noises just before impact.

What lesson do I take from this close call with death? My hero Isaac Asimov—who wrote over 500 books in his life—was asked what he would do if told he had only six months to live. His answer was “type faster.” Sounds like good advice to me!

Our car, after the accident.