INFORMATION FOR ATTORNEYS > Back To Newsletter List

Shaw Chiropractic
A Medical-Legal Newsletter for Personal Injury Attorneys
by Dr. Steven W. Shaw

Restitution In Motor Vehicle Collisions: No, I Don't Mean Monetary

I am often questioned about low velocity injuries and why property damage and occupant injury are often disproportionate. I have addressed this in several past newsletters but in this newsletter I will review one of the most important factors; RESTITUTION.

Lets start of by defining restitution. For our purposes, restitution is an object=s reaction to energy that is transferred from another object at collision. This reaction can vary significantly. The relationship between the object=s reactions is measured as the co-efficient of restitution and is recorded between 0 and 1. It is mathematically expressed as Ae@. The formula below demonstrates the mathematical formula for restitution:

e = Vs/Vc
(V=velocity, s=seperation, c=closing)

The coefficient of restitution is more or less a measure of elasticity. Collisions with high restitution coefficients are said to be more elastic. Lesser restitution coefficients are said to be more plastic.

This concept is relatively simple for a physicist but may be more difficult for us common people, particularly a juror. Therefore, it is important to paint a mental picture of this relationship so that a common person can appreciate the significance of this law of physics. The most commonly used education tool is the visual example of billiard balls versus clay balls

Picture in your mind two billiard balls on a pool table. The balls are of equal size, shape and mass (density). When the first ball (bullet vehicle) strikes a stationary ball (target vehicle) the stationary ball rapidly accelerates to nearly the same speed as the striking billiard ball. The striking ball rapidly decelerates to a near stop. This type of collision is mostly elastic and would approach a coefficient of restitution of 1.

Now visualize two clay balls of equals size, shape and mass (density) when compared to the billiard balls. These clay balls are not rigid like the billiard balls and when they collide they crush somewhat and roll away at equal velocity. This collision is much different than the billiard balls and has a restitution coefficient of close to 0.

In the real world it is nearly impossible to have restitution values of 1 or 0. Rather we have relatively elastic or plastic collisions. In high speed collisions restitution plays an insignificant role since vehicle crush results in restitution close to 0. However, in lower speed collisions, when there is little crush and high restitution , elasticity plays a significant role.

The importance of restitution in low speed impacts lies in the transfer of energy through the principles of conservation of momentum. Since there is little to no crush (vehicle damage) there is a rapid transfer of energy in the form of acceleration to the target vehicle. Injury results from acceleration of the target vehicle which in turn results in occupant acceleration of greater magnitude. The magnitude of acceleration between vehicle and occupant is as low as 1:2 and as high as 1:10. Therefore, a high restitution (elastic) collision which results in a vehicle acceleration of 3 Gs may result in occupant head acceleration between 6 and 30 Gs. This magnification of acceleration accounts for much of the injury causation in low speed collisions.