Low-Speed Accidents and Minimal Force Causing Bodily Injury
Patrick Sundby, Accident Investigator
Mark Studin DC, FASBE(C), DAAPM, DAAMLP
Citation: Sundby P., Studin M. (2019) Low-Speed Accidents and Minimal Force Causing Bodily Injury, American Chiropractor 41(7) 44, 46, 48-49
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.[1]
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.
The math looks like this:
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. (See below)
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.[2]
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.
References:
2. 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
[1] There is a change at the beginning and end of the maneuver, good for you if you recognized this!
Image Credit: Wikipedia Commons
[2] There are some variances in the results and the graphs, this is a prime example of rounding and/or truncating throughout the calculations.
Low-Speed Damages and Injuries
Patrick Sundby, Accident Investigator
Mark Studin DC, FASBE(C), DAAPM, DAAMLP
We have discussed the fallacy of “no damage = no injury” in depth in other papers, but as a reminder, we are interested in the relationship between injury and force experience, not damage induced. The phrase “no damage, no injury” is no more than “deceptive rhetoric” and draws a false causal relationship because it is based in subjective interpretation, dogmatic beliefs and too often, who is paying for your opinion. The extent of the damage, as viewed by each person, varies based on each person’s perspective. For example, what color is the square on the left?
What color is the square on the right?
The majority of the viewers of this article should say the squares are blue, but is it possible someone else sees the colors differently? What if this article was read in print form in black and white? What if the screen settings on a reader’s computer were out of adjustment? What if a reader has a condition which alters the way they see certain colors?
Taking the last variable, if the person with the condition sees the squares as something other than blue, are they wrong? No. To him/her, they genuinely see something else. This example demonstrates the subjective interpretation of the two colors presented to you in the squares.
So how do you resolve this subjective approach to the colors? You need to use an objective standard to gauge the colors against thus allowing you to determine if the colors presented are indeed blue.
In the electromagnetic spectrum, there is a small window in which visible light is located.
Within this small window, modern science has defined the wavelengths of different colors.
Rather than debating the colors of the two squares we can measure the wavelengths and compare them to the objective standard if both squares measure between 450 and 495 nm (nanometers) then both squares are indeed blue.
In the same sense of objectively defining colors, we need to objectively define the relationship between damage and injury. This relationship is defined, objectively, through force. If we can quantify the forces exerted on the vehicle (and by extension the occupant), then we can objectively compare those forces to known standards for injury. This MUST BE the method for defining the causal relationship between a vehicle collision and occupant injury vs. relying on dogma, rhetoric and financially influenced opinions because it relies on physics and the inherent mathematical facts.
Imagine being in a high-risk category for cancer and when at an appointment the doctor stands back, looks you up and down - while clothed, and says “you don’t look sick therefore you don’t have cancer.” This is the same practice when reconstruction is done via an insurance estimate. Ask yourself, how can you possibly know the extent of the damage to a vehicle when you didn’t even remove the bumper cover? When we consider the recent Allstate’s “QuickFoto Claim” where you take a picture of the accident, and they send you a check is a brilliant business move. The unsuspecting claimant thinks that getting a check quickly is a resolution of the damages to their car without ever inspecting the damages below the “skin of the car.”
When considering transference of forces and potential bodily injury, after a complete vehicle exam is done, we can assign a known value for the vehicles change in acceleration. This process can take place via a few avenues. For the sake of this paper and topic, we are going to use the Coefficient of Restitution (CoR).
If we can determine the post-impact speeds, we can then mathematically work the pre-impact speed for the striking vehicle thus eliminating any unknowns. Finally, we can check the work and ask if the results appear reasonable. (Remember 30 divided by 100 is also .3)
Consider the following case:
In this event, we have a typical lower speed collision. This vehicle was rear-ended while stopped and the occupant suffered injury. Further, there is the ever-present claim that “little/no damage = no injury.”
There is clear damage to the bumper cover and rear liftgate as well as some panel fitment issues at the corners. I’m highly suspect if we examined the structure of the bumper, we would find more evidence of the collision, and this would further support an appropriate CoR. After an examination of the vehicle, we could reasonably assign a high CoR to this event and work backward to the striking vehicle’s impact speed. While this would be of interest and worth exploring, we have complete tasks similar to this in previous discussions. This collision is important as there is a second and more specific point highlight. Consider the interior shot of this vehicle.
Consider what the chunk of missing steering wheel tells us. First, we know your average person doesn’t have the strength to tear the steering wheel. We can conclude the force of the collision did this, but how? The occupant was holding the wheel when the vehicle was struck. The collision accelerated the vehicle forward, and the occupant did not move at the same time. Once the occupant had “stretched out,” (the slack or bent arms at rest was gone) the force of the collision was translated to the steering wheel through the occupant. The question is, how much force?
The forces experienced by the steering wheel would be whatever percentage of body weight the occupant had in the torso times the “g-forces” calculated. In simpler terms, if the upper body of the occupant weighed in at “X” pounds, the steering wheel experienced this weight times the g-force. Take a quick second and consider if you had the steering wheel in your hands, what could you do to break it in a similar nature? Jump in it? Have a friend hold one side and pull? What does it really take to do damage like this? This concept is a bit of a trick question, any answer you provide is subjective – lets objectively try to determine the forces at play. This is where you put aside pre-conceived “beliefs” and allow the mathematics of physics to render answers because there are no beliefs in math equations.
When we examine the nature of a low-speed event, we will have to determine the g-forces the occupant experiences. For this example, we will utilize the following the following equation:
Initially, it appears very high values can be substituted, and the formula would still be correct. However, this doesn’t pass a sanity test. While the striking vehicle is not provided, we are assuming it’s the same or negligibly different from the KIA. We know the collision is not 100% efficient so the post-impact speed of vehicle two being 10 mph is not reasonable. In the same sense, the post-impact speed for vehicle one being zero is also not reasonable. (WHY?) We are going to use eight and two, respectively.
If the KIA was accelerated to 8 mph (11.76 fps), we could determine the g-forces be 3.65 at the lumbar spine. We also know the forces experienced at the cervical spine can be two to three times more than the lumbar, 7.3 to 10.95, respectively. These forces greatly exceed a plethora of known standards for cervical spine injury.
The process we just went through provides an objective conclusion for the forces that acted on the vehicle, and ALL of these values are a reasonable fit for the damage profile.
There is one final consideration, the broken steering wheel. The occupant holding the steering wheel would have forces act on them differently likely resulting in different injuries or increasing the forces acting on the body. A case-by-case evaluation for each collision and each occupant is a necessity to thoroughly and accurately establish the objective relationship between the forces the vehicle experienced and the forces the occupant experienced – Indeed, “no damage = no injury” is a myth.
Conservation of Momentum:
Where does it go, Part II.
By: Patrick Sundby, Accident Investigator
Specializing in Low Speed and Catastrophic Crashes
Mark Studin DC, FASBE(C), DAAPM, DAAMLP
In the previous writing we explored the standards for vehicle integrity during low speed collisions. In this writing we will expand on Conservation of Momentum. If you have not read the previous article you are encouraged to do so. While it’s not necessary to read it doing so will assist you as this writing will build on concepts contained within. If you do not have it, please contact us and we will make it available to you.
Expand on Conservation of Momentum.
Remember we previously said “The momentum going into a collision can be accounted for in the outcome” when we discussed the concept of Conservation of Momentum. Here we will introduce the formula and walk through its components; we will need to understand this in order to explore how different size vehicles affect each other in a collision.
The full formula:
Let’s walk through this, on the left side of the equation we have which is the weight of the first vehicle before the collision multiplied by which is the velocity (in feet per second) of the first vehicle before the collision. is the weight of the second vehicle before the collision times which is the velocity (in feet per second) of the second vehicle before the collision. On the right side of the equation we have which is the weight of the first vehicle after the collision multiplied by which is the velocity (in feet per second) of the first vehicle after the collision. is the weight of the second vehicle after the collision times which is the velocity (in feet per second) of the second vehicle after the collision.
Ok, I know this seems very complex and the explanation is not jumping off the page so let’s write with a little more ease of understanding. Let’s take the National Highway Transportation Safety Administration (NHTSA) standards for testing and put two of the same mass vehicles in this. Let’s use a 2012 Toyota Corolla, and because we need two of them we will say one is red and the other is blue.
Red Corolla * 5 mph + Blue Corolla * 0 mph = Red Corolla * 0 mph + Blue Corolla * 5 mph
The 2012 Toyota Corolla has a curb weight of 2,734 pounds, substituted in the formula it looks like this:
2,734 lbs * 5 mph + 2,734 lbs * 0 mph = 2,734 lbs * 0 mph + 2,734 lbs * 5 mph
We need the speeds in feet per second, to do this we will multiply by 1.47 times the miles per hour. This gives us 7.35 feet per second.
2,734 lbs * 7.35 fps + 2,734 lbs * 0 fps = 2,734 lbs * 0 fps + 2,734 lbs * 7.35 fps
Now when we do the math to show the conservation of momentum we end up with the following:
20,094.9 + 0 = 0 + 20,094.9
20,094.9 = 20,094.9
Momentum conserved.
Now we have proved the concept so we are going to apply it to a collision involving two different vehicles. We will substitute the 2012 red Toyota Corolla for a 2012 red Chevrolet Tahoe. The 2012 Chevrolet Tahoe weighs 5,448 lbs. Now the formula looks like this:
Red Tahoe * 5 mph + Blue Corolla * 0 mph = Red Tahoe * 0 mph + Blue Corolla * 9.96 mph
5,448 lbs * 5 mph + 2,734 lbs * 0 mph = 5,448 lbs * 0 mph + 2,734 lbs * 9.96 mph (speed after impact)
We need speeds in feet per second, to do this we will multiply by 1.47. This gives us 7.35 (5mph) and 14.64 (9.96mph).
5,448 lbs * 7.35 fps + 2,734 lbs * 0 fps = 5,448 lbs * 0 fps + 2,734 lbs * 14.64 fps
Now when we do the math to show the conservation of momentum we end up with the following:
40,042.8 + 0 = 0 + 40,042.8[1]
40,042.8 = 40,042.8
Momentum conserved.
Three important points can be observed in this demonstration.
First, when testing is done note the change in speed in the Tahoe is 5 mph (5 to 0). This is less than the speeds used by the Insurance Institute for Highway Safety which we have previously discussed and we would expect the Tahoe to have no structural deformation and minimal cosmetic damage.
The second point to note is the change in speed the Corolla experiences, 9.96 mph (0 to 9.96). This change in speed is four times the minimum needed to induce whiplash injury.
Finally, neither vehicle exceeds the speed of 10 mph, which the auto manufactures and insrunace institute for highway safety often consider threshold for injury. This confirms that cars can easily deform and occupants get injured in low speed crashes once you begin to look at the conservation of energy (momentum) and coefficient of forces transferred to the target car.
Should you want a further explanation or to discuss a case, please contact me 571-265-8076
Edmunds.com. (2012). 2012 Chevrolet Tahoe Specifications. Retrieved from Edmunds.com: www.edmunds.com
Edmunds.com. (2012). 2012 Toyota Corolla Sedan Specifications. Retrieved from Edmunds.com: www.edmunds.com
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, 72-80.
Patrick Sundbyhas decades of experience in the automotive industry including several years in law enforcement collision investigation. He has also been a driver training and firearms instructor in law enforcement and a police officer for 9 years before specializing in accident investigations. He has had the privilege of participating in both learning and teaching at Prince William County Criminal Justice Training Academy in Virginia and studied at the Federal Law Enforcement Training Center in Georgia. His specialty is low speed and catastrophic crashes and has testified over 500 times at various level. He can be reached at 571-265-8076 or patrick.sundby@gmail.com
Dr. Mark Studinis an adjunct associate professor of chiropractic at the University of Bridgeport College of Chiropractic, an Adjunct Professor of Clinical Sciences at Texas Chiropractic College and a clinical presenter for the State of New York at Buffalo, School of Medicine and Biomedical Sciences for postdoctoral education, teaching MRI spine interpretation and triaging trauma cases. He is also the president of the Academy of Chiropractic, teaching doctors how to interface with the legal community (www.DoctorsPIProgram.com). He teaches MRI interpretation and triaging trauma cases to doctors of all disciplines nationally, and studies trends in health care on a national scale (www.TeachDoctors.com). He can be reached at DrMark@AcademyofChiropractic.com or at 631-786-4253.
[1] If the formula is completed with rounded numbers the answer is 40,025.76 not 40,042.8. The full numbers are not shown, but used, to ensure a match at the end of the equation.
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[1]. 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)[2] 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)[3] 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.
REFERENCES:
Patrick Sundby has decades of experience in the automotive industry including several years in law enforcement collision investigation. He has also been a driver training and firearms instructor in law enforcement and a police officer for 9 years before specializing in accident investigations. He has had the privilege of participating in both learning and teaching at Prince William County Criminal Justice Training Academy in Virginia and studied at the Federal Law Enforcement Training Center in Georgia. His specialty is low speed and catastrophic crashes and has testified over 500 times at various level. He can be reached at 571-265-8076 or patrick.sundby@gmail.com
Dr. Mark Studin is an adjunct associate professor of chiropractic at the University of Bridgeport College of Chiropractic, an Adjunct Professor of Clinical Sciences at Texas Chiropractic College and a clinical presenter for the State of New York at Buffalo, School of Medicine and Biomedical Sciences for postdoctoral education, teaching MRI spine interpretation and triaging trauma cases. He is also the president of the Academy of Chiropractic, teaching doctors how to interface with the legal community (www.DoctorsPIProgram.com). He teaches MRI interpretation and triaging trauma cases to doctors of all disciplines nationally, and studies trends in health care on a national scale (www.TeachDoctors.com). He can be reached at DrMark@AcademyofChiropractic.com or at 631-786-4253.
[1] Some factors are acknowledged but not discussed for ease of concept explanation.
[2] 1 mph = 1.47 fps, 2.5 mph * 1.47 = 3.7 fps
[3] 1 mph = 1.47 fps, 6 mph * 1.47 = 8.8 fps
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