When evaluating what is commonly called "low speed" rear end collisions it is important to understand the limitation and assumptions inherent in the data and approaches used. Many errors exist in determining impact speed and occupant injury potential in these types of impacts. These errors range from the inappropriate use of damage, to misapplication of the laws of physics to the promulgation of non existent thresholds. A partial list of the errors to be addressed are shown below and discussed in detail in the paper.

1. The occupant motion described is often incorrect.
2. The comparison of rear impact with backing into a barrier is incorrect.
3. The correlation of staged volunteer tests to on road collisions is inappropriate.
4. Many underlying approaches for model validation are based on the propagation of an equation that is not valid in vehicle-to-vehicle collisions.
5. The common use the barrier data is not supported by the laws of thermodynamics.
6. The data the use to validate the models is often improper.
7. Using only one vehicle to determine impact speed introduces significant errors.
8. The use of cost data is inappropriate.
9. The references cited often refute the conclusions asserted.
10. The often stated injury threshold is not based on an accepted methodology and is refuted by readily available data.
11. Many investigators and authors fail to include identified aggravating factors in their attempt to establish an injury threshold.

It is not uncommon for an investigator to provide a technically incorrect description of the occupant motion in a rear impact. As an example, a reader often sees the following:

"During a rear-end impact, the occupant of the target vehicle is propelled into his seatback as the vehicle accelerates forward."

This is incorrect. The occupant obeys Newton's First Law of Motion¹ and remains stationary until acted upon by an outside force. The seat is propelled into the occupant. While the distinction may seem minor, it is critical to understanding the injury mechanics. This motion results in the torso being pushed out from under the head and the cervical column undergoing extension. The neck remains in extension until the head overtakes the torso and then moves into flexion. The torso does not experience rebound until interaction with the seatbelt².

Based on the information listed above, backing into a wall is not biomechanically the same as a rear impact. When a vehicle is backed into a wall, the occupant experiences extension and ride down. There is very little cervical flexion. In a true rear impact, there would be significant flexion. A simple analysis of the velocity curves of the vehicles in each case would show that there is no reasonable reference frame where the curves are the same shape. In a rear impact, the vehicle accelerates significantly and then decelerates significantly. In a barrier impact, the vehicle decelerates significantly and then accelerates minimally. Figures 1 and 2 show the velocity profiles of a vehicle struck from behind and one that impacts a wall. It is obvious that the shapes of the curves are not the same. Often an investigator will cite high numbers for volunteer tests such as; "one subject experienced a change in velocity of 6 or 8 m.p.h." Upon further research it is usually discovered that the referenced test is a non standard configuration and is not a true rear end collision.

Figure 1	Figure 2

The comparison of the injury potential of on road collisions to staged, safety optimized motion tests is unscientific for multiple reasons. In crash tests, safety is optimized. Often the volunteer is a healthy young male. Sometimes special seat belts are used. Bite blocks are often employed to prevent injury to the teeth and jaw. The test subject is aware that the crash is going to occur. The test subject is positioned to receive the forces of the crash. The subject is usually looking straight ahead and sitting upright. In the few cases where a crash subject had his head turned, the injuries suffered were significantly worse. The sample size in crash tests is quite small. These tests are fairly expensive, therefore, the number of vehicles employed and the number of test subjects used are limited. The statistical accuracy of these tests is questionable considering the number of vehicle speeds that are tested and the various vehicle impact angles that need to be evaluated. This uncertainty is compounded by the variations in the human body's tolerance to injury as a function of age, gender, position in the seat, and possible predisposition to injury as a result of prior medical problems. Even some of the authors of these tests state that they cannot be extrapolated to the general public. Many of the tests used researchers as subjects.

Many authors use programs that are a variation, or have similar assumptions as found in CRASH3³. In addition to the assumptions, commonly the equations used incorporate a error that has affected all subsequent models. Specifically, a fundamental assumption in many approaches, which attempt to equate speed and damage, is that acceleration distance equals crush distance. As an example, Ojalvo, et al. replicated this error in their 1998⁴ paper. This error, while obvious, is not well known. This error is one of the basic reasons that most models fail in collisions with minimal vehicle damage. The assumption is valid only as a first order approximation in barrier impacts.

The reason this, and other assumptions exists, is to simplify the problem. In a situation where nothing is known, there are at least 10 critical variables⁵. These must be determined or an independent equation must be used for each unknown. Since this has significant limitations, the equations are simplified to remove unknowns. This results in simplifying assumptions.

A partial list of simplifying assumptions found in many approaches that are not valid include,

• The vehicle acts like a mass with a spring
• The spring constant "K" is constant
• Only plastic deformation occurs.
• K1 = K2
• Equal crush occurs on both vehicles.
• The system acts as a simple harmonic oscillator.
• Total symmetry

Commonly, the approaches used then allow the user to violate the simplifying assumptions by varying the crush depth, the crush coefficient, the crush profile etc. This then generates the question, have the assumptions been violated to such a degree that the results are not relevant? The answer is usually yes. Numerous attempts have been made to validate the CRASH3 approach and its daughter programs. Typically, these validation attempts return 100% error rates, although in some cases it is infinite error. Figure 1 is a compilation of the results of one such test⁶. Error rates easily reached values approaching 100% in some cases and infinite error in others. It is worth noting that these tests were conducted under controlled conditions, not a circumstance normally found in actual collision. Other authors have also reported similar errors. Smith and Nagy⁷ reported errors rates of 50%. Wooley, et al.⁸ reported rates of 100%. Even the CRASH3⁹ Users Manual warns that:

"CRASH3 should be statistically valid for a large number of cases; it may or may not provide accurate results in a particular case."

Any approach derived from the equations used in the CRASH3 program is suspect.

Figure 1 - RICSAC Data

Many authors have correctly identified that the existing crush formulae are inaccurate for determining car-to-car crash closing speeds for impacts lower than 20 m.p.h. The fact that the formulae also have significant inaccuracies for speeds above 20 m.p.h. is based on the errors listed above. However, another of the reasons the formulae do not work is the misapplication of the principle of conservation of energy. The use of barrier data has this type of error.

By way of review, conservation of energy is logically obtained from the First Law of Thermodynamics. This law states that the total energy crossing a system boundary is equal to the change in energy inside the system¹⁰. This is often presented as an energy balance equation. For motor vehicle collisions the equation can be represented as:

(1) KE _pre-impact = KE _post-impact + C_rush E_nergy + Minor Terms

Where KE _pre-impact is the kinetic energy brought into the collision by the vehicles, KE _post-impact is the kinetic energy possessed by the vehicles after the collision and C_rush E_nergy is the energy dissipated through damage to the vehicles. The minor terms are energy sinks such as heat, noise, etc, and can generally be ignored. For this reason they are dropped from the discussion.

In a rear impact, such as that postulated by the authors, the equation becomes;

(2) KE (V1) _pre-impact + KE (V2) _pre-impact = KE (V1) _post-impact + KE (V2) _post-impact + C_rush E_nergy (V1) + C_rush E_nergy (V2)

Unlike momentum, energy is not a vector, having magnitude only. Many of the approaches available today attempt to look at the energy absorbed by damage to determine the speeds of the vehicles. This is significantly flawed since there is no direct mathematical correlation between energy absorbed by crush and energy retained or transferred as kinetic energy.

Many authors have attempted to use the dollar damage from barrier impact tests to determine the impact speed in a vehicle-to-vehicle collision. (The inappropriate use of dollar values is addressed below.) This approach will yield fundamentally erroneous results when compared with vehicle-to-vehicle collisions. With regard to energy, the inherent error in the approach proposed by the authors is obvious when the energy balance equation for a barrier impact is considered.

(3) KE (V1) _pre-impact = C_rush E_nergy (V1) + minor terms.

In this type of collision, virtually all of the energy must go into damage since the barrier is effectively an immovable object. While the minor terms still exist and contain some kinetic energy due to rebound from the barrier, it is clear that greater damage is expected in this type of impact since the majority of the energy must go into crushing the vehicle. The equation (3) becomes:

(4) KE (V1) _pre-impact = C_rush E_nergy (V1)

This explains why large vehicles fare so poorly in the IIHS¹¹ tests but do so well in an actual collision. The larger the vehicle, the greater the kinetic energy for a given speed. The greater the kinetic energy in a barrier impact, the greater the damage. The empirical data available proves what the laws of physics leads one to expect.

The National Highway Traffic Safety Administration (NHTSA) sponsors numerous tests each year on motor vehicles. While most of these tests are barrier impacts, it is possible to find vehicle-to-vehicle crashes. Four tests were obtained using Honda Accords¹². The vehicle to barrier test (VTB) was a frontal impact of a 1982 Honda Accord into a barrier at 34.8 m.p.h. The three vehicle-to-vehicle tests (VTV) used 1984 Honda Accords. These are sisters/clones of the 1982 vehicle¹³. Table 1 reveals that the average crush decreased in VTV impacts even when the kinetic energy of the vehicle heading into the crash increased by almost threefold. The reader is cautioned that there are too many possible impact variations to attempt a precise correlation between a staged test and an actual collision. However, the data in Table 1 does show that an attempt to assert that the damage from a barrier test can provide the velocity of the vehicles in car-to-car collisions has significant inherent error. The examples listed in Table 1 are at higher speeds than the authors of the paper implied they were dealing with. However, the design of bumpers is such that the affect of the protection provided by the bumper is expected to be greater at lower speeds. For example, vehicles that are damaged in 5 m.p.h. IIHS vehicle to barrier tests are usually not damaged in 10 m.p.h. vehicle to vehicle tests. This indicates a greater than four fold increase in energy is required to cause similar damage in the region commonly called "low speed".

In the initial attempt to validate a model based on damage, many authors will use data from vehicle to vehicle non-damage tests. This indicates that even if all of the other errors were remedied, the given model would only be applicable to no damage collisions.

As an example, recently Ojalvo et al presented an approach based on the cost of the repairs to a vehicle. The authors referenced their own paper¹⁴ and asserted that the results were favorable, further validating the simulation procedure. However, the paper did not list any damage to the test vehicles used to validate the claim. Other data suggests that these "validation" tests resulted in no damage to the vehicles. If this is so, then the attempt to extrapolate this approach to collisions with damage is unfounded.

Another common method of validation is to use case examples, often litigation related, to establish that a model is working. The authors reconstruct the collision using their model and then if the results are consistent, they claim validation. However, if an approach is repeatable but always produces an erroneous result, it is not legitimate nor an accepted validation method. The authors have merely established that their approach produces results; they do not in any way established that their approach yields valid results.

It is not uncommon to see a speed determination based on the damage to a single vehicle in a two vehicle collision. This approach is based on a misapplication of Newton's Third Law of Motion and will produce the minimum speed only, not the maximum. Newton's Third Law states that for every action, there is an equal and opposite reaction. Note that the law does not say identical reaction but rather equal. In a collision, the forces at the interface must be equal. The effect of the forces can be dramatically different. Figures 2 and 3 show two vehicles immediately after impact. Examination of the bumper on vehicle 2 revealed that the initial collision was bumper to bumper. If only vehicle 2 were used to determine the impact speed, the actual speed would be significantly underestimated.

Figure 2 Bullet	Figure 3 Target

It is not uncommon to find individuals attempting to determine the impact speed of a vehicle by comparing the cost of repairs. As will be shown below, the use of cost data for speed determination correlation invalid. The approach should compared actual damage to remove the affects of distortion due to variations in component costs, variations in regional costs throughout the country, variations in costs over time and variations in costs for non OEM parts.

Additionally, small variations in impact configuration can result in significant variations in damage, and therefore cost, in collisions occurring at the same speed. Data from Neptune Engineering shows NHTSA tests at virtually identical speeds with significant crush variation. As an example, two tests on a Chevrolet Celebrity at the same speed had a 16% variation in crush depth¹⁵. Furthermore, two adjacent components can easily have a cost differential measured in thousands of percent¹⁶.

This leads to a subsequent problem in the approach used by some individuals to determine speed. The source of the cost data is often IIHS and it has been reported that the IIHS removes the bumper to check for damage. A damage estimator for an insurance company rarely does this. In many cases, damage can only be found after the removal of the bumper system. This is the reason that supplemental repair estimates are common. As an example, with a foam core bumper, it may appear that the damage is limited to the bumper cover. Upon removal of the bumper cover, it is often found that the reinforcement is also damaged, significantly raising the cost of repairs. For illustration, when the reinforcement and associated structures on a 2004 Ford Mustang are considered, the repair estimate for the vehicle would more than double when compared with the bumper cover alone¹⁷. Figures 4 and 5 show a vehicle where the damage is not apparent from an external inspection.

Figure 4	Figure 5

Figure 6 shows a bumper cover with apparent superficial damage. Figure 7 shows the damaged bumper reinforcement. If the bumper were not disassembled, the damage would not be apparent. When speed determination is from repair estimates, caution must be used to ensure that the damage is fully documented. With the use of a damage estimate alone, only minimum speed can usually be determined.

Figure 6 Bumper Cover with minor damage

Figure 7 Bent Bumper Reinforcement

At the lower speeds, the empirical evidence continues to support the assertion that barrier impacts are a poor indicator of damage in vehicle-to-vehicle collisions. Virtually universally, the IIHS data reveals damage in 5 m.p.h. barrier impact tests. Equally universally, full-scale tests almost never reveal damage in 5 m.p.h. impact tests. The reason for this dichotomy is obvious when the energy balance equation is considered.

Authors often reference full-scale crash testing to support an opinion that the injuries alleged in a collision are not reasonable since other people have been tested and not injured. Usually these tests are cited in collisions where there is damage. This technique is to determine a low change in velocity, even in the presence of damage, and then compare the change in velocity to human subjects in no damage tests. One study often cited is the work of McConnell, et al¹⁸. In these tests, impacts were performed at 8 m.p.h. with no damage detected. Another common study is the work of Szabo, et al¹⁹. In these tests, six, 10 m.p.h. impacts were performed with no damage to the vehicles.

Additionally, many authors like to reference the work of West et al²⁰. These tests were divided into series A through D. In series A, a tow truck with a steel push bumper impacted a 1979 Plymouth Horizon twelve times at increasing speeds up to 7.2 m.p.h. At the highest speed, and after eleven previous impacts, one tail light was broken. In series B, a 1975 Pontiac Ventura impacted a 1977 Saab 99GL seven times. No damage was reported after the first five tests including one at over 10 m.p.h. After the seven impacts, three tests over 10 m.p.h., the damage reported was buckling to the Saab's rear quarter panels. In series C, a 1975 Pontiac Ventura was driven backwards into a rigid barrier. The rear bumper sustained residual damage in an impact in excess of 4.8 m.p.h. In Series D, a 1984 Volvo 760 was rolled backward into a concrete barrier. Damage was observed after a 4.5 m.p.h. impact. The trend overall demonstrated greater damage at lower speeds for barrier impacts when compared with vehicle-to-vehicle collisions. The one minor exception to this was in Series D when a light vehicle, a 1981 Ford Granada withstood damage until a 9.6 m.p.h. impact.

Another study commonly referenced is the work of Siegmund²¹ et al, testing specific automobile bumpers. In this study, damage was not reported in collisions resulting in a change of velocity in excess 9 m.p.h. The list of studies available to show that vehicle-to-vehicle collisions rarely produce damage with impacts under 10 m.p.h. is extensive. Smith²² for example, tested Ford Festivas and found only very superficial damage at 11 m.p.h. In reviewing the references cited by authors, it is not usually apparent that any of the studies resulted in damage at impact speeds below 10 m.p.h. However, these same authors use assorted methods to produced speeds below 10 m.p.h. for collisions with significant damage.

The approach used by many authors implies that injury probability can be determined for individuals based on the amount of damage to the vehicle. The authors use the kinematic studies referenced above to opine that testing indicates that normal, reasonably fit males can sustain rear impacts with changes of velocity up to 6 m.p.h.

This is not logically sound. It is well established that there are individual variances as well as variances in collisions. Assuming that there were only 16 binary variables, the number of permutations is 65,536. Sixty-five thousand tests have not been run. However, in reality, the quantity of variables is much larger and they are not all binary. The actual number of permutation is easily in the millions. Therefore, to take a controlled test and infer an injury threshold is invalid.

Contrary to the notion of an injury threshold are the injury databases that refute a threshold. As an example, NASS data presented by Dr. Murray Mackay at an SAE TOPTEC²³ established the absence of an injury threshold. His data is reproduced in Figure 6.

Figure 6 NASS Injury Rates in Rear Impacts, with permission, Murray Mackay

This data clearly shows that there is no threshold for injury. Many proponents of the injury threshold fail to incorporate any of the many injury studies that are available that would establish that there is not an injury threshold. For example, the Smith²⁴ paper showed injuries at below the "threshold." Typically, authors attempted to compare fundamentally dissimilar events.

Any discussion of an injury threshold without mention of identified aggravating factors is simplistic and incomplete. For example, it is well established that women are more likely to be injured than men^{25,26,27,28,29}. Another factor is predisposition to injury^30,31. Yet another is awareness of the impending impact. In most staged tests, including those previously referenced, symptomology began to appear at changes in velocity of approximately 5 m.p.h. However, in the Siegmund³² study where most, but not all awareness was removed, symptomology occurred at changes in velocity of approximately 2.5 m.p.h. Other factors include rotation of either the vehicle or the occupant and the effects of seat belt usage.

Caution must be used when considering the argument that it is possible to look at the visible damage to a vehicle and determine if the occupant was injured. The approach is flawed in many ways. Despite the references and discussions of the validated models, typically the approach is not based on any legitimate scientific or engineering approach. Commonly, results do not appear to have been validated by an accepted method. A true validation requires testing under controlled conditions, not relying on case studies an author might have been hired to reconstruct. Numerous questions often go unanswered such as; were the vehicles actually examined? Were the bumpers removed?

Careful evaluation of an approach often reveals significant errors and mistakes such as the use of damage estimates and comparing costs and the improper use of barrier impact tests. The results reported are usually inconsistent with published test results from numerous sources including the author's own references. The assertion of an injury threshold is unsupported by the references of the authors and is refuted by readily available data.