Little speed (mph) does NOT equal Little injury
When considering bodily injury, too often rhetoric or false perception “rules the day” in spite of sound conclusions based upon the mathematics in physics. This is commonly seen in Independent Medical Examination, Defense Medical Examination and in the courtroom. When assigning causality in the clinical setting, most doctors experienced in the diagnosis and management of trauma cases have concluded their patient's bodily injuries are directly related to the specific trauma, but don’t have the tools to render an accurate rationale. To demonstrably conclude the transference of forces from the bullet car to the target car and then to the occupant, you must first understand and then apply the principles of the “forces” involved. There are several components to discussing the forces applied to the occupant in a collision and here we will discuss the two most important, the quantity of forces delivered and how the force is applied.
The quantity of the force? What do we mean when we say that? There are a lot of different scales one could use, so we need one which is reasonably universal and applicable. For this we use “g-forces.” G-Force is a relationship to gravity which can be easily quantified to any event of motion. The odds are good you (the reader) are sitting in a chair, the chair exerts a force on you to keep you from falling to the floor, this force is 1 g. You will experience this force for the entire time you are seated, which opens the second part of the discussion – time.
The g-forces you experience are one part of the issue, the time it takes to experience the force is the second part. Imagine flying in a military jet fighter and the pilot banks the plane into a turn. You will experience an increase in force on your body which is related to the angle of the bank and the radius of the turn – most importantly, you will experience this increase in force for as long as the plane stays in that flight path. If the force is 4 g’s and the plane maintains that path of travel for 10 seconds you will experience the force evenly over the 10 seconds. In most of this example the time doesn’t change.
What happens when there is a time change? What happens when that same fighter jet lands on an aircraft carrier and the arresting wire take the plane from 200 miles per hour to zero in less than 4 seconds? The forces that are translated to the human body (what you feel) can be quantified in g-forces. The calculation is not quite as simple as multiplying the g forces against the time, rather we need to know the change in speed over the change in time. For the sake of discussion let’s say the slowest approach speed for the jet fighter landing on the carrier is 100 mph (147 fps) and it takes 4 seconds for the plane to come to a complete stop.
147 fps 36.75 fps/s
______ = 36.75 fps/s ________________= 1.14 g's
4 s 32.2 fps/s (gravity)
Although we commonly say g’s (meaning g force), there is no unit with this number, rather it’s a ratio of force acceleration against gravity (which is also acceleration) and the units divide out leaving us with just the 1.14. If we were in the plane in the scenario above, we would experience 1.14 times the force of gravity, 1.14 g’s.
We can apply this concept to starting to move from a complete stop. If were sitting in traffic, stopped, and we were struck from behind we would go from zero to a certain speed – let say 8 mph (11.76 fps). If the time to be accelerated took .1 or 1/10th of a second, we can also calculate the g-forces experienced by the occupant and then determine the injury potential.
The provided value of 3.65 g’s (in the calculation below) is the relationship experienced at the seat base and is not the same force experienced at the skull. We know the research shows the cervical spine and the skull experience approximately three times the force of the hip – why?
As the vehicle begins to move and so does the occupant’s hip, the skull however, isn’t moving just yet. After all the “slack” in the lumbar and thoracic spine is used the skull and cervical spine are all that’s left, and it takes time to use the slack in the lumbar and thoracic spine resulting in less time for the cervical spine and skull. As a demonstration of concept – if we said it takes 66% of the 1/10th of a second to load the lumbar and thoracic spine then 33% of the 1/10 is all that is left for the cervical spine and skull. This changes the calculations:
When we divide by 32.2 fps/s, we end up with 12.17 g’s at the cervical spine and skull. Notice this is almost exactly three times the initial 3.65 g’s at the hip.
The graph below visualizes the forces experienced. The orange line is the force experienced at the cervical spine if twice the lumbar, the grey line is the force experienced at the cervical spine if three times the lumbar spine.
Now that we have explored the quantification of forces applied, let's look at how the forces act on humans. Below is a graph which depicts the forces experienced in everyday events as well as the collision we discussed earlier in this writing (8 mph at .1 seconds).
Consider how the forces on the bottom of the slide can act on a human, is coughing a natural act? Why is it then that the cited reference, (Brault et al 1998) can establish injury to the cervical spine and we can quantify that value at almost the same as coughing? By this comparison coughing and a rear-end collision at 2.49 mph should result in almost the same injury every time. Why then are doctors and hospitals everywhere not overrun with patients who have cervical spine injuries from coughing?
The answer is HOW the forces are applied to us! Walking, sneezing, coughing, hopping, sitting in a chair, etc. are actions we, as humans, are biomechanically designed to do. We do these things every day with no negative sequelae. However, when you sit in a vehicle and you are struck from behind nothing about that action mimics an activity which is normal to us. Being accelerated from behind in a short amount of time, such as a car collision, is not a natural action and not something we are designed to do.
When considering traumatic bodily injury to the human spine, advanced knowledge of spinal biomechanical engineering and spinal function at both the global and regional scale is a necessary requirement. Advanced knowledge is inclusive of the resistive forces of connective tissue attachments, bony stabilizing mechanisms and central nervous system (brain) innervation for both the guarding and the compensatory aspects of the body’s response to injury. Additional application of the principles of physics regarding the forces applied to the occupant in trauma, gives the provider a scientific rationale for causation and bodily injury devoid of false perception and rhetoric. The combination of spinal biomechanical engineering knowledge and an understanding of the physics of the forces applied will resolve most questions of fact and provides a demonstrable answer when assigning the cause of bodily injury.
1. Brault J., Wheeler J., Gunter S., Brault E., (1998) Clinical Response of Human Subjects to Rear End Automobile Collisions, Archives of Physical Medicine and Rehabilitation, 79 (1) pgs. 72-80
2. Siegmund, G. P., King, D. J., Lawrence, J. M., Wheeler, J. B., Brault, J. R., & Smith, T. A. (1997). Head/neck kinematic response of human subjects in low-speed rear-end collisions. SAE transactions, 3877-3905
3. Sundby P., Studin M. (2019) Low-Speed Accidents and Minimal Force Causing Bodily Injury, American Chiropractor 41(7) 44, 46, 48-49