Where:
a = acceleration
V = velocity
of impact
s = the
crush distance
Let's examine
two different situations to illustrate this concept. In the first situation,
we have a car that hits a solid brick wall at 10 mph (4.46 meters/sec) and
crushes the front of the car 5 inches (.127 meters). In the second scenario,
let's keep the at speed 10 mph, but because of a different car design, the
crush in this instance is only 2 inches (.0508 meters).
In the
first example a is found to be 78.3 m/sec2 (4.46 x 4.46/2 x .127), or 8
Gs of force.
In the
second example a is found to be 196 m/sec2 (4.46 x 4.46/2 x .0508), or 20
Gs of force.
Thus, a
collision with the same velocity, but with a crush amount smaller by 2.5
times will have a resulting G force 2.5 times larger.
The author
sums up this relationship as it relates to whiplash-type injuries:
"…on
a vehicle with a chassis, no serious visual deformation may occur even though
it is subjected to relatively high speeds of impact. Classically, we see
this in the case of pickup trucks or all-terrain vehicles that are traditionally
fitted with a solid bumper-to-bumper chassis. Many of these types of vehicles
are subjected to relatively severe impacts with little or no resulting damage
to their bodies and bumpers. The classic whiplash injury associated with
a great deal of litigation is most likely founded on the reasoning that
if there was little or no vehicle damage, no injury can result. Motor vehicle
bodies or bumper-to-bumper chassis offer little or no crushing effect on
arresting obstacles when impacted; thus, relatively high G forces can be
experienced by occupants when rear-ended, resulting in whiplash injury.
The use of stiff motor vehicle bodies and chassis will also produce a spiked
G force loading to occupants, even if little damage occurs to vehicle body
or chassis."
The graph below shows the relationship between crush distance
and G forces, and as we can see from this chart, vehicles that do not crush
can experience very large accelerations at low speeds.