Conservation of Momentum:
Where Does the Energy Go, Part 1
By: Patrick Sundby, Accident Investigator
Specializing in Low Speed and Catastrophic Crashes
Mark Studin DC, FASBE(C), DAAPM, DAAMLP
There are many factors which play a role in the dynamics of automotive collisions. These include vehicle design and type, speeds, angles of approach, kinetic & potential energy, momentum, acceleration factor, friction… the list is very long. However, there are a few constants in which we are most interested. These constants are the building blocks of our world and they make the chaotic world of automotive collisions predictable and quantifiable.
In this two-part series we will explore the factors which have the most influence in low speed collisions and how these factors are related to injury. Note: nothing about these writings is inclusive, there is simply too much material to explore, much less explore in depth. The goal of these writings is to introduce the concepts to you.
In this writing the topic of exploration is Conservation of Momentum and how it relates to low speed collisions and bodily injury of the occupant. Conservation of momentum is built on Sir Isaac Newton’s third law. Newton’s third law states “For every action there is an equal and opposite reaction”.
In the interest of exploring conservation of momentum in a simple format, we are not going to explore and explain the history and physics of momentum; for this conversation, we will focus on the relationship to crash dynamics. It is the relationship of momentum to low speed collisions that is the causal factor of the injuries and helps enlighten those who have held tight to the deceptive argument that no damage = no injuries.
While there is a formula and derivation, neither is needed just yet. For now, we will simply use the concept as follows: The momentum going into a collision can be accounted for in the outcome or the energy going in to the accident, must be accounted for at the end of the incident and who and what was exposed to and/or absorbed that energy.
Let’s apply some perspective to the concept with the following example.
Let’s say we are standing at around a pool table and we are going to attempt the winning shot of the eight ball into a corner pocket. After the cue ball is struck, we now have one object in motion which will collide with another. When the cue ball strikes the eight ball, it stops moving and the eight ball begins moving. In this scenario the momentum of the cue ball before the collision is the same as the momentum of the eight ball after the collision. The eight ball rolls into the corner pocket.
The transfer is highly efficient due in part to the fact that neither pool balls can deform. If either pool ball could deform, some of the energy would be used to do this and less would be transferred to make the ball roll. The National Highway Transportation Highway Safety Administration (NHTSA) mandates minimum performance standards for passenger vehicle bumpers. Vehicle bumpers are tested with 2.5 mph (3.7 fps) impact equipment which has the same mass as the test vehicle. The test vehicle is struck with its brakes disengaged and the transmission in neutral. There is no offset between the vehicle and the barrier.
The NHTSA outlines acceptable damage to a vehicle’s various systems after the tests. Successful completion of these tests mandate normal operation of certain systems. The factory adjustment of the vehicle’s braking, steering, and suspension must be unaltered. In other terms, in order for a vehicle to pass these tests it cannot have any change in its structure. If changes did occur the braking system, steering, and suspension would be out of factory adjustment.
The NHTSA is not alone in low speed bumper testing. The Insurance Institute for Highway Safety (IIHS) also conducts low speed bumper tests. The IIHS’s test speeds are conducted at 6 mph (8.8 fps) and the goal is to determine which vehicles have the least damage and therefore cost the least to repair. The vehicle ratings are inversely proportional to the estimated cost of repair. The costlier the repair, the lower the rating, exclusive of safety.
While the vehicles used in the IIHS testing all show signs of contact with the barrier, none of the vehicles suffer damage which deforms the structure of the vehicle. Just as with the NHTSA the vehicles tested by the IIHS do not have any change in its structure affecting the braking system, steering, and suspension.
The lack of change in the structure (deformation) forces a test vehicle to accept the momentum transfer from the testing equipment. Further, the test vehicle is free to move after being struck. This testing scenario is strikingly similar to that of the cue ball and eight ball.
If a vehicle doesn’t deform during a low speed collision, then it will experience a change in speed (or velocity) very quickly; Accordingly, the occupant(s) also experience this same change in speed. The key factor in these examples is the equal mass of the vehicles and testing equipment involved, but what happens when the masses change?
When the mass of one vehicle changes the momentum also changes, the more mass the more momentum the vehicle can bring to the event and the greater the injury potential to the occupant. There are many complicating factors that now must be considered regarding injuries beyond the Laws of Momentum when determining injury such as the height, weight, muscle mass, occupant position, type of seat belt used, etc. However, the first step is to determine if there was enough energy as an initiating factor in low speed crashes to cause those injuries and to overcome those no crash = no injury misconceptions and then have a medical expert in low speed injuries confirm causal relationship.
In the next installment, part II, we will discuss this in detail and it will necessary for the later topic of occupant injuries.
 Some factors are acknowledged but not discussed for ease of concept explanation.
 1 mph = 1.47 fps, 2.5 mph * 1.47 = 3.7 fps
 1 mph = 1.47 fps, 6 mph * 1.47 = 8.8 fps