WINTER 2012 | VOL. 1, NO. 1
Older Workers Not So Bad: NCCI
Prescription Drug Abuse on the Rise
When Small Cars Meet Big Cars
Profile: Church & Co. Adjusting
Special Report | AUTO INJURIES
David Versus Goliath Revisited
What Happens When Small Cars Meet Big Cars on the Road?
By Donald Parker
S
mall cars have always been with us, but with new incentives driven by the high level of fuel prices in the past few
years, automobile manufacturers are introducing a swarm
of small and even “micro” cars to an eager buying public.
With modern, robust construction and materials, and the
latest safety technologies in place, these new small-car entries are
in many cases able to attain high marks in federal and insurance
crash safety ratings.
Yet what do the laws of physics dictate when “David” meets up
with “Goliath” on the road?
In a certain light, history is repeating itself.
In 1973, the first Arab
oil embargo caused fuel
shortages, quickly escalated gas prices and led
the U.S. Congress to first
enact Corporate Average Fuel Economy (CAFE) standards.
Car sales subsequently stalled, and automakers responded with
aggressive plans to introduce smaller and lighter cars. By 1985, cars
were an average of approximately 500 pounds lighter than their
predecessors.
In subsequent years, fuel was again relatively inexpensive, and
average car size crept back up. The light truck market of sport utility vehicles (SUVs), pickups and vans grew dramatically, eventually
surpassing cars in volume.
Unprecedented fuel price increases in 2008 triggered a collapse
in large car and light truck sales, and led Congress to mandate the
most aggressive fuel economy standards in history. In 2009, the
fleet CAFE standard was set at 35.5 miles per gallon (mpg), to be
achieved by 2016. In 2011, the standard was updated and set at 54.5
mpg, to be achieved by 2025.
Every major auto manufacturer responded by rushing to
introduce small cars to meet customer demand and federal CAFE
requirements.
While it has long been common public perception that the size
and weight of a large car generally equates to a safer car, this issue
may become somewhat confused by the advent of safety ratings issued by federal and insurance organizations based on crash testing.
The two most common and publicly accessible ratings are issued
by the National Highway Transportation Safety Administration
(NHTSA) and the Insurance Institute for Highway Safety (IIHS).
NHTSA issues ratings of between 1 and 5 stars, which signify
a statistical risk level of occupant injury in a given crash scenario,
with 5 stars being the best rating.
IIHS gives a rating of poor-marginal-acceptable-good, based
partly on occupant injury risk, but also based on subjective evaluations of vehicle structural performance and occupant movements.
These ratings are based on crash tests conducted primarily against
a rigid barrier, or a 3,000-pound moving barrier intended to simulate another vehicle in side and rear impacts.
There can be no doubt that cars today are safer than ever before
because of the continuous development of safety features, including
seat belts and pretensioners, a variety of air bags and side curtains,
electronic traction, braking and stability controls, adaptive headrests, high-strength structural materials, and other technologies.
Even so, certain physical laws of nature prevail. It comes down to
Newton’s Second Law of physics;
F = ma
The change in velocity versus time (acceleration) of an object is
directly proportional to the force applied, and inversely proportional
to its mass.
For frontal crash evaluation particularly, testing is typically
done using a rigid barrier. In a simplified sense, the car crashes
into the barrier at some predetermined speed and comes to a stop.
The change in the vehicle’s speed, in this case to zero, is commonly
called the “Delta-V.” In a rigid barrier crash, the Delta-V is theoretically the same as the pre-crash speed (See Figure 1: Understanding
Delta-V Vehicle Speed on right).
In reality, the Delta-V will
actually be a bit higher because
the car has a certain amount of
spring-back or restitution, and
will bounce away from the barrier at a reduced speed. Think of
dropping a ball of soft putty (very
low restitution) and a golf ball (high restitution) to the floor, and
the difference in how high they bounce.
In the formula of F=ma, acceleration (a) can be equated to:
Therefore, Delta-V is proportional to the acceleration. In the
absence of intrusion into the passenger compartment, the Delta-V is
generally an effective indicator of the severity of the collision for the
vehicle’s occupants. That is, low Delta-Vs relate to low forces and
lower injury risk, higher Delta-Vs relate to higher forces and higher
injury risk.
Newton’s Third Law of Physics dictates that the forces of action
and reaction between any two interacting bodies are equal, opposite
and collinear. What this means is that in a given rigid barrier crash
test, the car is in essence crashing into the equivalent of an identical
car traveling at the same speed in the opposite direction. Everything
matches up; they come together in the middle and basically stop.
Where it gets more complicated is when the two vehicles coming
together are not identical. This article only addresses mass issues.
Size and proportional issues, such as bumper and structure height,
crush space and stiffness compatibility are complications worthy of
lengthy discussion on their own.
For simplicity, it is also assumed that in cars, “small” equates
to “lighter” and “big” equates to “heavier.” Take, for example, the
approximate curb weight of two recent products available on the
American market: a 2009 Mercedes C-Class sedan and a 2009 Smart
car (See Figure 2: Approximate Curb Weight). No endorsement or
criticism of either product is intended, they just are two products
from the same manufacturer that had similar safety ratings, yet very
different size and weight characteristics. Both were given safety ratings by both the NHTSA and the IIHS (See Figure 3 Safety Ratings).
As noted, Newton dictates that the forces in a collision are equal
and opposite. So while the forces acting on the two vehicles are
equal, the masses are not — thus the accelerations are not, either.
From Formula 1, the acceleration is inversely proportional to the
mass. Laws governing Conservation of Momentum come into play.
In its simplest form, laws of linear momentum dictate that:
Where W1 and W2 are the weights of vehicles 1 and 2, V1 and V2 are
their respective velocities, and V3 is the velocity of the combined vehicles, stuck together after the impact like balls of putty. For simplicity,
this ignores any restitution effects, and in essence says that the velocity
of the combined vehicles is equal to the sum of the weight of each vehicle
multiplied by its speed. This affects a collinear frontal or head-on crash
in cars with mismatched weights.
In a hypothetical collinear frontal or head-on crash between a C-Class
and a Smart car (See Figure 4: Momentum Effects in a Frontal Crash), the
speed of each car is 40 mph, so the closing speed is 80 mph. Due purely
to mass and momentum effects, the post-crash speed of the combined
vehicles is 13 mph in the direction the C-Class was heading, with the
Smart car being pushed toward the rear.
While the heavier C-Class experiences a Delta-V (acceleration) of 27
mph, the lighter Smart car experiences a Delta-V of 53 mph, nearly twice
that of the C-Class. The acceleration experienced by the Smart car during
the collision would be higher by the same proportions. Restitution would
tend to increase the Delta-V on each car by a few miles per hour, as the
cars bounce away from each other a little.
The same simplified physics applies easily to a collinear rear crash as
well as a frontal crash (See Figure 5). In a situation where the C-Class rearends the Smart car at a closing speed of 40 mph, again ignoring restitution,
the C-Class experiences a Delta-V of 13 mph while the Smart Car experiences a Delta-V of 27 mph — twice that of the C-Class (See Figure 6).
The numbers illustrate that what happens in a crash all relates to the
weight of the vehicles; the C-Class weight is approximately twice that of
the Smart Car. The Delta-V for each vehicle is inversely proportioned to
its weight. While both cars have similar safety ratings in collisions with
solid barriers, the physics is stacked against the small car in a collision
with a heavier car.
This is reflected in testing reported in an April 2009 IIHS Status Report
(Volume 44, Number 4). In that testing, a frontal crash test with a C-Class
Mercedes and a closing speed of 80 mph resulted in the Smart car being
given a “poor” rating, as compared to a “good” rating based on a 40 mph
barrier crash test. As explained, the barrier crash test roughly simulates a
frontal crash into another Smart car at a closing speed of 80 mph.
The bottom line is that while safety ratings such as those posted by the
NHTSA and the IIHS are important and useful indicators, it must also be
taken into account how they are developed and what they truly represent. From basic physics, in most collisions between a small car and a big
(heavier) car or light truck, the small car occupants will be exposed to
greater impact accelerations than those in the heavier car. Consequently,
occupants of a small car likely will be exposed to greater injury risk. CJ
Parker is a principal with Exponent Inc. in its Detroit-area office. He spent
more than 20 years designing and testing automotive products, with an additional 17 years investigating, researching and reconstructing real-world
crashes and evaluating vehicle crashworthiness performance.
Reprinted with permission from Claims Journal, Winter 2012. On the web at
www.claimsjournal.com.
© Wells Publishing, Inc. All Rights Reserved. Foster Printing Service:
866-879-9144, www.marketingreprints.com.
www.exponent.com
[email protected]
248 / 324-9100