Velocity and acceleration In general terms, as the velocity of a crash increases, so too does the risk to life and limb. In a crash, one of the factors that injures or kills is the kinetic energy of that crash. From Newton's second law of motion we can derive an equation for kinetic energy as follows:

Kinetic energy equations.

where KE is kinetic energy, m is mass, and v is velocity (or w is weight and g is the force of gravity; 32.2 ft/sec2). From this it is clear that kinetic energy increases with the square of the velocity, or, as the velocity of a crash doubles, its kinetic energy quadruples. So, clearly, velocity is a very important consideration in a crash. On the other hand, nearly everyone has heard of a crash in which one occupant was killed, while another walked away with only scratches. Similarly, health care practitioners who are experienced in treating persons injured in motor vehicle crashes often see a broad range of injuries among persons traveling in the same vehicle. Thus, while velocity is an important factor in crash risk, it is not the only important factor, nor is it usually the most important factor. When speaking of crashes, there are a number of ways to express velocity. These are defined below.


Impact velocity This is a term commonly used to describe the speed of a vehicle that strikes another vehicle. In the parlance of crash traumatology, the striking vehicle is often referred to as the bullet vehicle and the struck vehicle as the target vehicle. This term can be misleading, though, because if the bullet vehicle is traveling at a speed of 20 mph and the target vehicle is traveling at a speed of 15 mph in the same direction, the closing velocity or differential velocity (i.e., 20-15) would be only a quarter of the impact velocity.

Closing velocity (differential velocity) This is simply the difference between the two colliding vehicles and is a more meaningful term when discussing crash phenomena. In the prior example, the closing velocity would be 5 mph (20-15 mph). In the case of a head-on crash, the velocities would be added.

Change of velocity (delta V) The change of velocity is an even more useful term in crash phenomena, because it tells us what happened to the colliding vehicles as a result of the crash. It is influenced by a number of factors, such as vehicle masses. Delta V also plays a major role in auto crash reconstruction, particularly in low velocity crashes, because many have come to believe that injury risk can be directly linked to delta V. In the case of low velocity crashes, however, this link has poor predictive value. Moreover, the relationship between delta V and injury risk is not entirely linear. Within a narrow range of low velocity crashes, the risk can actually be lower for higher speed crashes and higher for lower speed crashes because of the relative stiffness of low velocity crashes. Once the crash velocity reaches the point where vehicle crush begins to occur, the crash becomes more plastic and has a longer duration. When the duration of the crash is increased, the acceleration will be decreased. This is evident from the following equation:

a=delta V/delta T

where a is acceleration in ft/sec2, delta V is velocity change in feet/second, and delta T is the duration of the change of velocity in seconds. This is an extremely important concept in crashworthiness because, while it is not always possible to decrease the velocity of a crash, it is sometimes possible to increase the duration of a crash, thereby reducing the acceleration and reducing the risk for injury. For example, if a person were to jump from a 10 story building onto a concrete sidewalk below, the sudden acceleration at the end (which would really be deceleration or negative acceleration) would not be survivable. If a stunt man were to make the same jump, he would plan to land on a special air mattress into which air is pumped and which also has vents to vent air when he lands on it. The overall effect is to allow a controlled deceleration. Note that the delta V is the same as the person landing on the sidewalk. The only difference between the two-and the one that is critical to understand crash trauma-is the duration or delta t. When the duration is increased, the acceleration is decreased to a tolerable level. In the parlance of crash traumatology, by increasing the denominator of the equation above by increasing the duration of the crash, we say that the stunt man rides down the crash.

There are many examples of ride down. The laminated glass and plastic of a car's windshield will bow about 5 in when struck with sufficient energy by an occupant's head. If a person were to strike that windshield with his head at a speed of 25 mph, he would experience about 50 g of acceleration. If, on the other hand, he were to strike the metal frame outside the windshield, which provides only half an inch of ride down, his head acceleration would be an order of magnitude higher-500 g, and that would not be survivable: the same crash in both cases, but two very different outcomes. Another familiar example is race cars. When an Indianapolis Racing League type car hits a barrier at high speed and is virtually demolished, the driver often emerges unscathed. This is possible because these cars are designed to deform, crush, bend, and break in such a way as to reduce the driver's acceleration and improve his survivability. Even the barrier he crashes into is designed to absorb energy. It takes energy to damage the vehicle and barrier and that energy is no longer available to injure the driver.

Estimating injury risk from property damage As a result of the elastic nature of low speed rear impact crashes (LOSRIC), the apparent paradox of the inverse relationship between property damage and injury potential is a real one. According to research from the Peugeot S. A./Renault Laboratory of Accidentology and Biomechanics, the risk for whiplash injury is actually greater below 9.3 mph than above it. Previous attempts to correlate these factors have failed to show a strong relationship. Walz and Muser (Walz FH, Muser MH: Biomechanical aspects of cervical spine injuries. SAE Tech Paper Series 950658 45-51, 1995) concluded that, "The greater the vehicular damage, the less the biomechanical loading (and the inverse)." Outcome studies, in which researchers have attempted to correlate the outcomes of injury (i.e., who recovers vs. who has long-term symptoms or disability) with the extent of property damage have also not shown a significant relationship. In a recent LOSRIC study conducted in New York, the largest category of injury crashes were graded as having no damage. In these, 38% of females and 19% of males had symptoms. When damage was rated as minor, these percentages were 54% and 34%. So there is some relationship, but it does not allow us to rule out the possibility of an injury when there is no property damage.

But let us be perfectly clear and unambiguous here, because there is much confusion over this issue. When speaking about the entire spectrum of crash scenarios-from the most trivial bump to the 100 mph crash into an immovable object-one would be correct and justified is claiming that there is a correlation between crash velocity and risk for injury. However, in the context of lower speed crashes ranging from 2 mph up to 10 mph, this correlation tends to be obscured by the many other variables that can either mitigate or enhance the risk for injury and for poor outcome. Variables of sex, age, awareness, positioning in the vehicle, prior medical condition, etc., often have more influence than the speed alone and this is why researchers have not been able to make a direct correlation between velocity and risk. Moreover, acceleration can vary widely over a broad range of speed changes, yet is a more important determinant of risk.

But let us be perfectly clear and unambiguous here, because there is much confusion over this issue. When speaking about the entire spectrum of crash scenarios-from the most trivial bump to the 100 mph crash into an immovable object-one would be correct and justified is claiming that there is a correlation between crash velocity and risk for injury. However, in the context of lower speed crashes ranging from 2 mph up to 10 mph, this correlation tends to be obscured by the many other variables that can either mitigate or enhance the risk for injury and for poor outcome. Variables of sex, age, awareness, positioning in the vehicle, prior medical condition, etc., often have more influence than the speed alone and this is why researchers have not been able to make a direct correlation between velocity and risk. Moreover, acceleration can vary widely over a broad range of speed changes, yet is a more important determinant of risk.

Relative mass The relative mass between two colliding vehicles is an important determinant of the outcome. Mass figures prominently in equations describing kinetic energy and in those describing momentum. In general, when a larger vehicle crashes into a smaller vehicle, the occupants of the smaller vehicle are at greater risk of injury or death. They will experience generally higher delta V and higher acceleration. This is true across a wide range of crash conditions, from rear impact crashes to very high speed head-on crashes. However, as noted earlier, there are many variables which affect injury or death risk.

The relative risk of fatality for an occupant in a car that collides with a car that is 50% heavier are as follows: for 1966 through 1979 cars, the risk is from 3.7 to 5.1 times higher; for 1984 cars, 2.6 times higher; and for 1990 cars, 4.1 times higher. One study found a positive correlation between risk of injury in CAD trauma and the relative weight of the two involved vehicles. For all crashes, analysis of the U.K Cooperative Crash Injury Study data shows that among occupants of smaller cars the rates of MAIS 3+ injuries were twice that of larger car occupants.

Crush characteristics A number of human subject crash tests have been conducted in the recent past and from these, it can be seen that modern passenger vehicles, engaged in rear impact crashes at low speeds can withstand crashes with closing velocities of 8-12 mph without sustaining appreciable property damage. (See table below.)

Damage Thresholds in Tested Cars: Rear Impact Crashess
Year of Study Vehicle Closing Velocity
1993 1975 Pontiac Ventura 4.8 mph
  1977 Saab 99GL 10.1 mph
  1981 Ford Granada 8+ mph**
  1984 Volvo 760 4.8 mph
1992 1981-3 Ford Escorts 10.0 mph**
  1980 Chevy Citation 8.4 mph*
  1977 Honda Civic 8.2 mph*
  1980 Toyota Tercel 8.1 mph*
  1981 Ford Escort 10.2 mph*
1991 1979 Pontiac Grand Prix 9.9 mph*
  1978 Honda Accord 11.0 mph*
  1983 Ford T-bird 11.7 mph*
  1989 Chevy Citation 12.4 mph*
  1979 Ford E-150 van 9.9 mph*
  1979 Ford F-250 P/U 12.1 mph*
1997 1999 Honda Accord 10.0 mph**
1996 1976 Volvo 242DL 10 mph**
2002*** 1991 Lincoln Continental 9.9 mph**
  1991 Honda Civic DX 7.2 mph
  1989 Ford Tempo GL 7.0 mph**
  1992 Chrysler Le Baron 9.9 mph**
  1994 Hyundai Excel 7.2 mph
  1992 Ford Taurus 7.7 mph
  1996 Chevrolet Cavalier 5.9 mph**
  2000 Chevrolet Impala 8.7 mph**
  1994 Ford Taurus 7.5 mph
* delta V, not closing velocity** multiple impacts without damage*** Croft AC, Herring P, Freeman MD, Haneline MT: The neck injury criterion: future considerations Accid Anal Prev 34;247-255, 2002.

In the crash testing engineering literature, one can find the terms barrier equivalent velocity (BEV), energy equivalent speed (EES), or equivalent barrier speed (EBS). All are more or less synonymous and refer to crashing a car into a fixed, non-yielding barrier. EBS can be used by auto crash reconstructionists (ACRs) to estimate the pre-impact speeds of crashed vehicles by measuring the intrusion or crush at various points and plugging these measurements-along with stiffness and other values specific for the vehicles in question-into empirically-derived equations which are based on regressions of crash test data (i.e., crush in inches and crash velocity). The raw data for these regressions is from a narrow range of crashes in which cars are run into rigid barriers to satisfy Federal Motor Vehicle Safety Standards. However, cars colliding with rigid barriers behave differently than when colliding with relatively softer and movable cars. A rigid barrier, as the name implies, does not deform. Another car, however, will. Moreover, these formulas are not entirely valid in the lower ranges of vehicle damage because they assume a linearity which does not exist.

Direction of impact The point of impact is an important factor in risk assessment in crashes of any velocity. The largest proportion of motor vehicle crashes are frontal crashes. Rear impact crashes make up only about 25% of reported traffic collisions. However, within the lower collision ranges, rear impact crash is far more likely to result in injury. In one study, regarding whiplash injuries from motor vehicle crashes (MVC), 48% were of the rear impact variety, while 24% were front end, 17% were roll-over, and 11% were side impact. In a series of 34 chronic whiplash cases, another study reported 82% rear impact, 12% frontal impact, and 6% side impact. In a series of 137 neck injuries from MVC, it was found that the majority were attributable to frontal or side impacts (76%) vs. rear impacts (23%), but that at one year follow-up, patients involved in rear impact MVC were more likely to be symptomatic (32% vs. 24%).

In a report of German data 17% of car occupants received cervical spine injuries and 50% were the result of rear impact collisions. In another German report (n=10,735 injured occupants) rear impacts accounted for 50.2% of all injuries. Another group reported that rear end collisions accounted for only 3.9% of their group, but were associated with 18.2% of the injuries. Another large study (n=3927 injured occupants) found that rear impact trauma was associated with four times the risk of injury as frontal or side impacts. In a smaller group of patients (n=38) it was reported that 68% were injured in rear impact collisions as opposed to 21% and 11% for frontal and side collisions. A slightly larger prevalence of neurological injuries will be found in rear impacted persons. An overall neck injury rate of 16% has been reported in the UK, but rear impact crashes carried a risk of more than double that (38%). However, significant underreporting was likely in that study.

In one study rear impact vector crash CAD injuries accounted for 64% of all sick leave days from MVC-related injuries. In a Norwegian study, 75% of the patients studied for MVC-related neck sprain were injured in rear impacts. In another study by these authors, those injured in rear impact crashes recovered at a lower rate than those injured in other vector crashes. Croft et al. at the Spine Research Institute of San Diego were the first to document and quantify some of the collision related factors that are likely to best explain the differences in risk between frontal and rear impact crashes (see Croft AC, Haneline MT, Freeman MD: Differential occupant kinematics and head linear acceleration between frontal and rear automobile impacts at low speed: evidence for a differential injury risk. International Congress on Whiplash-Associated Disorders, Berne, Switzerland, March 9-10, 28, 2001; and Croft AC, Haneline MT, Freeman MD: Differential Occupant Kinematics and Forces Between Frontal and Rear Automobile Impacts at Low Speed: Evidence for a Differential Injury Risk, International Research Council on the Biomechanics of Impact (IRCOBI), International Conference, September 18-20, 2002, Munich, Germany, 365-366). They found that subjects in rear impact crashes are exposed to a more complex, biphasic occupant kinematic, experience a rapid change in direction of the head within a fraction of a second, have less ability to brace, and, because of the head striking the head restraint, experience up to three times the head peak acceleration compared to subjects in the bullet vehicle, all other factors held constant.

Side impacts are some of the most dangerous of collision vectors because of the lower structural protection offered by car sides and because of the relative aggressiveness of most vehicles' front end components. Making matters worse, of course, is the disparity between vehicle masses, ride heights, and structure (i.e., frame rail design vs. unibody or monocoque). Increasing ride height and mass of the bullet vehicle have been shown experimentally to result in deeper penetration of the target vehicle and greater potential for injury. The most important factor in side impact crashes is the match-up between the longitudinal components of the bullet vehicle and the door sills of the target vehicle. If the door sill of the target vehicle is too low or the longitudinal components of the bullet vehicle are too high, intrusion will be significant. In recent years, manufacturers of several SUVs have been lowering the front ends and moving from longitudinal (truck) frame rail construction to a unibody construction to reduce this risk. One U.K. study reported that the mean delta V for a side impact fatality crash was 30 mph.

It has recently been shown that, overall, contacts with the opposite side of the car interior and with safety belts were the most frequent causes of AIS 3+ injuries in far side crashes (i.e., crashes on the side opposite the occupant). The presence of an occupant on the near side changed the injury pattern of the far side occupant, mitigating injuries from contacts with the opposite side interior of the vehicle.

The growth of the utility type vehicle fleet has been steady in recent years, with a fleet shift in light trucks and vans (LTVs) from 20% in 1980 to 35% by 1997. SUVs have seen a nearly comical expansion with nearly every make-including most luxury marques-entering the market, and they are also classified as LTVs. An analysis of U.S. crash statistics shows that, although LTVs currently account for approximately 1/3 of registered U.S. passenger vehicles, collisions between cars and LTVs account for over 1/2 of all fatalities in light vehicle-to-vehicle crashes. In these crashes, 81% of the fatally injured are found to be occupants of the car. Occupants of cars struck in near side crashes by full sized vans are 23 times more likely to die than the van driver. This is compared to a smaller 6:1 ratio for passenger cars struck by other passenger cars.

For more in-depth information of this topic, see Croft AC: Whiplash & Mild Traumatic Brain Injuries, SRISD Press, San Diego, CA, 2009, available from the Spine Research Institute of San Diego.