What is rigidity?
Rigidity is generally thought of as how stiff an object or a structure
is. For example, a garden hose is not very stiff or rigid. In
fact it bends under its own weight. However, a block of steel
measuring 4" on all sides is very rigid. Not only won't it bend
under its own weight, it also bends very little when force is applied to
A materials measure of stiffness
is called Modulus of Elasticity. Steel, for example, has a very high
modulus of Elasticity, whereas that garden hose, which is made of rubber,
has a very low Modulus of Elasticity.
However, just because a material
has a high Modulus of Elasticity does not mean it is 'stiff'. A thin
steel wire is not very stiff because it has a low Moment of Inertia.
The Moment of Inertia of an object is the sum of the products of each mass element of
the object multiplied by the square of its distance from an axis (usually
the center of gravity). In layman's terms, if all the objects mass
is located close to the center of gravity (think of the thin wire) it will
have a low Moment of Inertia.
By moving the mass away from the
center of gravity, you increase the objects Moment of Inertia. As an
example, a CART Champ Car chassis has a very high Moment of Inertia (both
bending and torsional or twisting) because, as can be seen in the photo
below, most of its mass is moved out to it extremities and the center is
Back side of a Champ Car
hollow area is where the fuel cell resides.
is twisting strain produced when a torque is applied to an object. For
example, torsion is the strain experienced by a length of wire when a
twisting force is applied to one end while the other end is fixed. Torsion
can be measured by observing how much an object twists due to a given
torque. For example, when a cylindrical object one unit long is twisted at
one end, and the other end is held fixed, the amount the ends of the
cylinder rotate relative to each other is a measure of the torsion.
Engineering materials employed in rotating machine parts, such as engine
crankshafts and ship-propeller shafts, must resist the torsional stresses induced by the twisting
loads. Whereas Moment of Inertia is a measure of an objects ability
to resist bending, Polar Moment of Inertia is the measure of an objects
ability to resist twisting.
measure of an objects strength is directly related to both its
Modulus of Elasticity and its Moment of Inertia or Polar Moment of
Generally, long slender objects are not rigid, and short stocky objects
are. The hollow steel tubing used to make a Winston Cup frame is, by
itself, not very rigid. It won't bend under its own weight like the
hollow tubular rubber garden hose will because steel has a much higher
Modulus of Elasticity than rubber, but it will bend when relatively very
little force is applied to it.
However, by making a space frame out of steel tubing, you can make a very
strong and stiff structure.
Tubing made into a space
protects drivers in violent crashes
Space frames are
generally very stiff structures even though the individual elements that
make up the frame, may themselves, not be very stiff. That is
exactly the case in a Winston Cup car steel space frame chassis
Earnhardt's fatal accident last week at Daytona, safety in racing has received
a lot of attention. A lot has been written and discussed concerning the HANS
Device because Dale Earnhardt died of a Basal Skull Fracture. I firmly support the idea that drivers wear the HANS Device, however, there is
another area of safety that needs to be addressed - Race Car Crumple
Zones. More specifically, should the concrete walls be made soft and
crumple, or should sections of the cars be made soft and crumple. That
is the issue this article will attempt to address.
Any race car designer will tell
you that the rigidity (see sidebar) of the chassis is a key component of a
good handling race car. A good chassis is one that offers good
torsional rigidity as well as transverse and lateral rigidity. A rigid
chassis allows weight to be transferred from one end of the car to the
other, from one side to the other, or diagonally from one corner to the
other (Called cross-weight transfer).
The most important measure of
torsional rigidity is how much stiffness there is from the center of gravity
of the car to the front axle and from the center of gravity to the rear
axle. This is part of the front weight transfer equation. If the distance
from the center of gravity to the front axle is larger than to the rear
axle you will have more front weight transfer (before springs and tires
various bars throughout a Winston Cup chassis space frame which gives it
strength and torsional rigidly.
Unfortunately, in an accident, a
very rigid structure does not crumple much and, therefore, much of its
Kinetic Energy is lost in a very short timeframe and the object decelerates
In recent years, the automotive industry has improved the crash worthiness
of passenger cars by the use of Crumple Zones in the front and rear of the
cars. Crumple Zones are created by the integration of variable
grades of steel and composites into the front and rear-end assemblies of the
automobile. These Crumple Zones yield during impact, redirecting the
energy of the collision, often reducing the chance of injury to the
This is best illustrated in the
two examples below. The first example shows a solid steel block
hitting a cement wall. The block does not crumple at all, stops almost
instantly, and rebounds or bounces off with almost as much Kinetic Energy as
it had just before it hit the wall. In the second example a Coke can
hits a wall. However it crumples and deforms just as if you stepped on
it, and much of its energy is dissipated over a period of time while the can
block hits wall, stops almost immediately with very high 'G' force
deceleration and rebounds. In physics terms, this would be
described as a very elastic impact. See this article
for an explanation of Kinetic Energy.
Coke can hits wall, but decelerates much slower while it crumples.
Because it crumples and decelerates over a much longer period of
time, it experiences very low 'G' force deceleration and rebounds with much less
energy. Energy is lost in the form of sound and heat. In
physics, this would be called a very inelastic behavior.
test. The front of the car crumples, but the drivers
compartment remains intact.
In an accident, the general goal is to keep the safety cell (where
the driver sits) intact at the highest speed possible without killing the
occupant, this implies that the safety cell has to be as stiff as possible (to avoid the
collapse of the safety cell and the intrusion of the wheels, engine or steering wheel
which can be deadly) and has to be surrounded by a crumple zone that is not too stiff
(the sudden deceleration would kill the driver instantly) nor too soft (useless, the
wall you'd hit would go right thru the crumple zone and you'd be killed anyway).
A trade-off has, therefore, to be found for the
strength of the crumple zone: at low speed (25mph for example), the car (car
#1) with a very soft crumple zone might inflict less damage to the driver than a car with a stronger crumple zone: the
driver would be shaken badly in the 2nd car, yet the driver "wouldn't feel anything" in the first car.
However, at 60 mph, the driver of the 1st car would probably be killed by the intrusion of the engine,
the steering wheel, etc. where in the 2nd car, because of the " extra margin"
allowed by the stronger crumple zone, the driver would probably be injured but still
A well designed
Crumple Zone, one which extends the time over which a car
decelerates, exponentially reduces the force felt by the driver.
It is, therefore, possible to find a car
(# 1) that manages to protect the driver better than car # 2 at a speed of
25 mph, yet car #2 could be safer than car #1 at a higher speed than 60 mph because
car #2 has a stronger crumple zone than car #1, allowing it a " last resort" extra safety
margin that the driver would not have with car #1.
That is why it is crucial to see how well the structure of a car performs in
a crash test. Only the one whose structure hasn't started to collapse will allow
the driver that extra safety margin in case of a stronger impact. Note that the size of the crumple zone is important : that is why,
in general, minivans (with shorter "noses") don't perform as well as cars in
frontal crash tests. So crumple zones have to be "attached" to the stiffest cell possible and
must not be too soft nor too strong!
Crash tests results have nothing to do with the weight of the car
tested. It has to do with how well the safety cell-crumple zone-restraint system combo have been designed.
So if you drive a very light car with good crash tests results into a wall, you will be better off in that car than in a truck, even 2 times heavier,
that would have "bad" crash tests results. However, if that truck hit the small car,
even though that car has better crash test results than the truck, you'd be better off in the truck because
of the weight difference. In general, you'd be safer in a heavy
vehicle hitting a lighter vehicle, regardless on how it performs
in crash tests.
What happened to Dale
people can't believe that Dale Earnhardt was killed at Daytona. The
accident just didn't look that severe. Unfortunately I don't have any
crash data to analyze because Winston Cup cars are not equipped with any
CRASH boxes that are found on CART Champ Cars, F1 cars and IRL Indy
cars. NASCAR is taking a lot of heat because of this. Therefore,
it's hard for us to determine exactly what happened. Yes, his seat
belt may have broken, and yes, the HANS Device very well may have saved
him. However, the fact of the matter is that the vector component of
speed that Earnhardt's car hit the turn 4 wall at Daytona was no more than
mph. Stop for one moment and think about driving your car into an
immovable wall at 55 mph. I would not want to try it, even if it does
have a crumple zone.
The one thing probably working
against Earnhardt was the fact that the front of Winston Cup cars have
become stiffer over the years in the search of better handling. In the
photo to the right (top), one can see that, when finished, the front
assembly of a modern Winston Cup car is relatively stiff compared to the
back (bottom photo to right). That is one reason why drivers typically
walk away unscathed in rear-end accidents - the backend of the car acts as a
Crumple Zone, absorbing kinetic energy in the form of heat and sound as it
folds up right to the back of the strong drivers compartment cage -
much like the Coke can did in the example above. However, on front
impacts, a modern Winston Cup car crumples up to a point near the front
wheels, after which the chassis becomes very stiff, upon which deceleration
becomes very rapid.
engine and transmission mounted in the chassis in the top photo.
Together they make for a relatively stiff structure. Compare
that to the relatively flimsy back of the chassis in the bottom
A properly designed front
Crumple Zone on a Winston Cup car would probably mean the end of cars going
back out on the race track after an accident just to collect points.
The front assembly would need to be designed to crumple in a more
predictable manner than it does
now. That would probably render the car unfixable at the race track,
or at least might require a nose change before re-entering the race. I think it's better to make the cars safer in an attempt to
save a drivers life, than to collect a few points trolling around the apron
of the race track for three-quarters of the race.
Soft Cars vs. Soft Walls
Typically, the most lethal
accidents are those in which a race car hits an immovable concrete wall and
the 'g' forces felt by the human body are not survivable. The crashes
you see when a car goes somersaulting down the race track tend not to kill a
driver because at no time does the driver decelerate too fast. While
the car is somersaulting, it's losing kinetic energy over a relatively long
period of time (seconds vs. milliseconds when you hit a concrete
wall). Therefore, the race car industry has to take a serious look at
the concrete wall impacts.
In order to lessen the blow to
the driver, we are going to have to make a concerted effort to develop an
acceptable 'soft' wall design, or we are going to have to design the race
cars with Crumple Zones. Both ideas have their problems:
Wall Challenges on oval tracks
to the track owners to outfit the many existing tracks
variable resistance needed for light open wheel cars vs. heavy 'stock'
potential for snagging a car because the wall will tend to pocket when
possible bounce back of a race car into traffic
walls ability to perform a 2nd or 3rd hit in the same race.
Crumple Zone Challenges
Design and testing that will
be required to make the front of the cars just stiff enough
Cost to the car owners to
make changes to all their cars
The possible tradeoff
between a stiff, good handling car,
and one that is a little more flexible but gets around the race track a
The possible need to
introduce space-age composite, energy absorbing materials, into the
front of what is essentially a 1950's designed unsophisticated tube
After studying this problem for
awhile, I am of the opinion that without a doubt, soft walls work well for road courses and the inside walls of oval tracks. They should be
implemented immediately everywhere. However, the outside walls of oval
tracks present a much different problem, and the jury is still out as to
whether a soft wall will work on outside walls. The sanctioning bodies
must step forward and start testing the various products out on the market
today to determine if a soft wall will work. It's too hard to model,
only real live testing with properly instrumented cars will tell the whole
If I had to guess right now, I
might lean toward making the crumple happen in the car rather than the wall.
What speed do you design for?
A lot of accident analysis has
been done looking at the geometry of most oval tracks. Unless a race
car gets down into the grass infield, the steepest angle the car could hit
the wall is 30 degrees (that is the angle of impact of the cg of the car
with the wall). In
Earnhardt's case his impact was probably more like a 20 degree hit. The SIN of 30 degrees is 0.5. That means
a car traveling at 100mph would be the equivalent of hitting the wall at
50mph head-on. The FIA standard test for soft walls is also about
50mph. Data has shown that most impacts with the outside concrete wall
are equivalent to a 50mph head-on impact, or less. As I stated above,
that's still pretty severe.
Compared to a
1950's tube frame stock car, a CART Champ car is made of space-age
composite materials. This view is looking down where the drivers
legs extend. The seat is removed. The first bulkhead you
see is about where the dash board is mounted. There is another
bulkhead further forward in front of the drivers feet. They have
about a 3' Crumple Zone in front of the drivers feet The
strength of that crumple zone is specified by CART to have a
predictable crumple force.
Using some of the equations for
energy from our previous article on safety, one
can determine what the size of a Crumple Zone should be. Let's
75 mph to give ourselves some margin of error.
An object in motion has kinetic energy. The magnitude of the kinetic energy depends on both the mass and the speed of the object according to the equation:
E = 0.5mv2
where m is the mass of the object and v2 is its speed multiplied by itself.
For a 3500 pound car traveling at 75mph (110 fps), E = 0.5 x 3500/32.17 x 1102
= 658,222 ft-lb.
The change in a
vehicles energy, ‘delta E’, can be derived from the equation:
= (m x a)d
where ‘a’ is
the acceleration (or deceleration, also known as negative acceleration)
applied to the mass, ‘m’, and ‘d’ is the distance through which
‘a’ acts. However, energy really does not enter into the
analysis, but force, distance and time do.
Newton's second law, F = ma
(3500/32.17) x (60 x 32.17), one can determine that same car
will apply a constant force of 210,000 lb. against the wall it is
hitting until it came to rest (assuming a linear deceleration). That force
would be needed to design a properly stiff Crumple Zone. The
time, therefore, it will take that same car to decelerate so that the
driver experiences no more than 60 g's is the change in velocity divided
by the deceleration or, 110 fps/(60 x 32.17) = 0.057 sec.,
or 57 milliseconds. That would be assuming that the Crumple Zone
applied a constant resistance until the car stopped. In reality the resistance
is not linear and the instantaneous deceleration is usually about twice as
great, hence the time of 57 milliseconds is only approximate and why we
used 75 mph for our analysis when in fact most collisions with the outside
wall are under 55 mph.
Assuming we don't want the driver to experience any
more than 60 g's (60 x 32.17 feet per sec2), an effective crumple zone in
any race car hitting a wall at 110 fps and decelerating linearly to zero,
regardless of weight, would have to be about
3 feet long (110 fps/2 x 0.057 sec. = 3.135'). That's assuming a
75mph hit. If we use a more practical number, about 55mph, the
distance is 2.3'. Another way to derive the same answer is to divide
the Energy computed above (658,222 ft-lb) by the derived constant force of
210,000 lb = that same 3.13 feet. Remember when your teacher tried
to tell you that Energy = Force x Distance? It's really true!
In round numbers
then, a properly designed Crumple Zone for a 3500 lb. stock car would be
about 2.3 to 3 feet long, be able to sustain a consistent force of 210,000 lb. for a period of at least 57 milliseconds, while
decelerating the car from 75 mph (component of speed of the cg of the car into the wall).
Although the nose of today's Winston Cup cars are about 3' long before
they crumple and the stiff part of the chassis is engaged, they crumple
too easy and, therefore, don't keep the deceleration under 60 g's for a
long enough period. Drivers are also
questioning NASCAR's decision last year to increase the strength of the front-end roll bars from 93-hundreths to 125-hundreths steel. The stronger
front-end bars could make the stiff part of the car less crushable. And there are complaints
about crews being allowed to use chrome-moly alloy in the bars; that makes for stronger bars, but
chrome-moly doesn't bend as easily as other
steel and can actually fracture. Plus if welding isn't done just right, the
welds can crystallize.
The challenge to NASCAR will be to add enough
resistive materials in the first 3' of the car so that it acts like a properly
designed Crumple Zone for the weight of their cars. And if that
means using some form of honeycomb composite materials to do it, then so
Racing will never
be a 100% safe sport, but NASCAR certainly has a lot of room for
improvement. And they can start with the noses of their cars.
NASCAR, are you