Kinematics, Part 1

By Dr. James Beauchamp, Multi-Specialty HealthCare

For the purposes of this article kinematics will be roughly defined as that chain of events which transfers energy from a moving motor vehicle into the body of the driver of another vehicle through a motor vehicle collision (MVC). This transfer of energy is what causes the injuries sustained in an MVC. A spinal sprain or strain (i.e. whiplash) can only occur if energy is put into the spine which results in an over stretch or too rapid a stretch of the tissues. In other words, flesh must be put into motion. We will trace the path of the energy from one vehicle into the body of the driver of another vehicle rear-ended at a stop light. In another article, we will delve into exactly how the energy causes injury to the driver of the stopped vehicle.

There are a few physics concepts that we must keep in mind. When I speak of the energy of the striking car I am referring to its kinetic energy (KE). Mathematically it is expressed as half of the mass of the car multiplied by the square of its velocity. The relative difference between the speed of the two vehicles increases impact energy more than the size difference between them. Although size does matter. The next concept is Newton’s first law of motion, which states that a body at rest or in motion will remain in that state unless acted upon by an outside force. A car travelling at 80 MPH would remain moving at that speed forever unless its KE were to be dissipated through external forces such as the friction of the road, the passing air and internal mechanical friction. Energy transformation is the essence of Newton’s second law of motion: Energy cannot be created or destroyed, but only transformed from one form into another. For example, a car braking to a stop gradually and safely transforms its KE into the heat of the brake rotors. The energy potential of an explosive transforms into sound and a blast wave upon detonation.

Automobile manufacturers design their cars to absorb part of the collision energy in order to reduce the impact that the vehicle occupants will be subject to. The first line of defense is the structure of the car itself. Crush zones around the perimeter of the vehicle are designed to absorb part of the KE of the striking vehicle through material deformation. This leaves less energy available to accelerate both the struck vehicle and its occupants. There is a limit to this strategy because the space immediately around the passengers must remain intact lest the crush extend into the passenger compartment. That circumstance can result in a high level of lethality. In our scenario, vehicle 1 (V1) rear-ends vehicle 2 (V2) while v2 is at a stop. The rear portion of V2 is crushed, partly defusing the explosive energy of impact. But more than enough energy remains to savagely accelerate the frame of V2, to which is attached the driver’s seat and its unfortunate occupant.

Up to this point the driver of V2 has remained motionless (Newton’s First Law) in the milliseconds in which his vehicle has already been crushed and accelerated forward. As the seat begins to move forward with the frame, the driver remains motionless while the seat padding collapses and the seat back is forced rearward. Once the drivers own inertia is overcome the seat acts like a catapult, throwing the driver violently forward with the combined force of the seat rebounding and the kinetic energy of the frame as it accelerates. There is so much KE in a rapidly moving car that no amount of passive or active safety systems can completely absorb the entire force of impact. For that to happen, V2 would have to be encased in a concrete block, in which case, by Newton’s Second Law, all of the KE of V1 would be expended upon its own destruction. The net result is an energy transfer: The KE of V1 has been imparted to the driver of V2, who now has a different velocity than his own car. As noted earlier, force must be applied to human tissue for injury to occur. The stage has now been set for the driver of V2 to be injured.

I would like to point out one fact that I have so far avoided. Namely, how in the world did the driver of V1 fail to see a traffic signal, let alone another vehicle in the road blocking his path? One would suppose that any driver would exercise the utmost caution considering that a moving vehicle has the destructive potential of a small bomb, with all of the potential for property damage and human suffering which that implies. And yet this is the single most common injury scenario that I see in practice. Ones actions impact the lives of others, sometimes literally, which make this a moral, not just a legal or biological issue. We will examine the nature of this impact in the next article.

Dr. James Beauchamp is a Multi-Specialty HealthCare provider specializing in Chiropractic Care. He is certified in spinal trauma, manipulation under anesthesia, and as an automobile accident reconstructionist. He is also a member of the advisory board for Operation Backbone.

Copyright James W. Beauchamp, DC | References available by request.