Xinmiao Yu
WRIT 340
Professor Elisa Warford
December 2, 2013
Re-designing Control Arm (A-Arm) with Carbon Fiber
Abstract:
Innovation in robust material development has been the quest of the century. While the
constant competition to devise the perfect material goes even beyond the boundaries of the
scientific and engineering community, there is clearly a winner when it comes to speed
contests. The persistent "Need for Speed" from the XBOX gaming corner to the racing track
of Formula SAE not only demands light-weight materials, but also requires the very
qualities like high strength and stiffness in them. Even though steel has been the material of
choice for its easy maneuverability and ‘historic significance’, carbon fiber has been the
most widely acclaimed winner of the "Material for Speed" racing track. In this paper, the
advantages, disadvantages, feasibility and cost effectiveness of using carbon fiber in a
Formula SAE racing car will be discussed and evaluated in further depth.
Introduction:
Formula SAE is an annual racing competition where student organizations from different
universities participate with a small scale Formula style race car. "Designing, building, and
racing" - these three words are probably the cornerstones of FSAE competition. From
ideation to design board, from CAD modeling to fabrication, from machining to lubrication,
from testing to tweaking, and last but not the least, racing and winning - all are blended
together in the SC Racing dream. A cliché definition of FSAE cars would probably go
something like this - "single-seat, open-wheeled, open-cockpit performance race car". SC
Racing is the official representative of University of Southern California in the FSAE
competitions held around the world (Michigan, Lincoln, Australia, Brazil, Italy, UK and
Germany). Teams are graded in the competitions based on their performance in different
areas such as presentation, design, cost effectiveness, acceleration, skid-pad, autocross, fuel
economy and endurance of the car.
Fundamentals:
Before diving into the world of carbon fiber, it is worth getting a good grasp of the
suspension system: a suspension system of a car is a system of springs, shock absorbers
and linkages that connects a vehicle to its wheels and allows relative motion between the
two.[1] Various geometries have been taken into account while designing the suspension
system for the FSAE cars. In this respect, the SC Racing Team uses the most widely used
design known as a Double Wishbone Design.
Figure 1: Front A-Arms in USC’s FSAE car.
The Double Wishbones, shown in Figure 1, are commonly called Control arms or A‐arms
because of their physical similarity to the letter “A”. The A-arms have the important task of
securing the wheel assembly to the chassis and they also play a key role in determining the
camber and roll stability of the car.[2] The key parameter to keep in mind while designing
the A-arm is the balance between weight, stiffness, strength as well as manufacturing cost.
Carbon fiber undoubtedly wins in the first three sectors; the last one might require design
optimization and a thorough cost analysis.
Advantages of Carbon Fiber:
USC’s SAE cars have been traditionally using steel made A-arms. But due to the potential
significance of the car’s performance enhancement, the SC Racing team is seriously
considering to transition from their current steel A-arm to a carbon fiber A-arm. The
carbon fiber A-arm would increase the performance at least in three different areas: lower
weight, higher strength and higher stiffness.

Low Weight:
From an aerodynamic perspective, it is the general consensus that the lower the
weight, the higher the performance. In the field of racing, where speed is
worshipped, weight can be considered an evil force or enemy. As a high
performance racing car, Formula SAE cars also require light weight to achieve high
acceleration and speed. Lower weight also comes with the benefit of fuel efficiency.
The weight of the car depends in part on the density of the materials being used.
Carbon fiber is a material that consists of fibers about 5-10 μm in diameter and are
composed mostly of carbon atoms.[3] The atomic structure of carbon fiber is similar
to that of graphite which consists of sheets of carbon atoms arranged in a hexagonal
pattern.[4] The difference lies in the interlocking of these sheets.[4] In graphite, the
sheets are stacked parallel to one another. The intermolecular forces between the
sheets are Van der Waals forces; that is why graphite is soft and brittle.[4] On the
other hand, carbon fiber is strong but still very light–weight which is one of the
biggest advantages of using carbon fiber in A-arms. The density of carbon fiber is
almost five times less than that of steel as well.

High Strength
The formula SAE car requires a high strength structural frame to withstand the
forces caused by acceleration, braking and turning. In order to fabricate qualified Aarms, it is very important that the A-arm meets the required criteria for strength
and stress. There are two types of stresses: the one most relevant for the A-arm
design is the tensile stress, which is the maximum stress that a material can
withstand while being stretched or pulled before breaking. This can be calculated by
the formula, F/A, where F is the tensile force, and A is the fixed cross sectional area.
In carbon fiber, the carbon atoms are bonded together in microscopic crystals,
which make it extremely strong. Carbon fiber materials are classified by the tensile
modulus of the fiber. The strongest carbon fiber has a tensile modules of 500 million
to 1 billion kPa, which is much higher than steel. [5] Typically, steel only has a tensile
modulus of about 200 million kPa. In other words, the strongest carbon fibers are
ten times stronger than steel, which means the carbon fiber can withstand ten times
larger force.[5] The other form of stress or strength is the compressive strength, c,
which is the resistance of a material to breaking under compression, and can be
calculated by the formula, P/A, where P is the compression and A is the area of the
cross section. The carbon fiber also has a very high compressive strength, which
strongly withstands deformation.

High Stiffness
Stiffness is the measure of rigidity of an object; in other words, the extent to which it
resists deformation in response to an applied force.[6] Stiffness is also an important
aspect of concern for the Formula SAE car design because the excessive deflection or
bending may affect the control systems and the acceleration mechanics drastically.
During high speed motion, if the A-arm is not stiff enough, the FSAE car will have
high roll in a turn, which could potentially cause loss of control on the wheels. That
is where carbon fiber comes into play. Its high stiffness could be the ultimate
advantage for the team on the track.
Disadvantages of Carbon Fiber:
The foremost disadvantage of using carbon fiber is that it does not yield much. When it is
compressed or pushed beyond its strength capabilities or exposed to high impact, it will
crack if a hammer hits it.[7] Machining and holes can also create weak areas that may
increase its likelihood of breaking. It is also more expensive than traditional materials
because working with carbon fiber requires a high level of skill sets and many difficult
processes to retain high quality.[8]
Possible Design Thoughts:
In designing the SC Racing Control arms with carbon fiber, in order to take advantage of all
its wide range of benefits, the best possible component to start with would be carbon fiber
tubes. As discussed above, a carbon fiber tube is extremely light-weight and also provides
sufficient stiffness and strength. But the complexity is to attach the carbon fiber tubes with
the chassis, which would definitely require further investigation. A simple solution could be
the use of very strong epoxy or glue, but that may not be sufficient since the components of
heat, speed, temperature etc. need to be taken into account. Attaching carbon fiber tubing
with steel parts would definitely require a thorough analysis of available adhesives in the
market and may require creative design modification as well as fabrication technique
optimization.
Current trends in Carbon Fiber use:
A few years back, the use of carbon fiber in the automobile industry was almost completely
limited to high-end racing cars or in the garage of millionaire auto-enthusiast. The reason
was clearly the high manufacturing cost of carbon fiber and the highly sophisticated
expertise required in order to mold this expensive material into a car. But several auto and
aerospace companies have taken initiatives to mass-produce carbon fiber in order to
fabricate a decently average-priced vehicle, which is certainly a step forward. From that
note, not only the suspension system, the entire car for the Formula SAE competition could
be built with carbon fiber. That may be something to keep in mind for future
improvements.
Conclusion:
From the aforementioned engineering analysis, it is pretty obvious that carbon fiber can
replace steel in any given day, but the ease of using steel may not disappear overnight. In
the Trojan family we care about winning, we care about our supremacy amongst other
teams and other schools. We will take steps in the right direction, and in the winning
direction. So it is probably time to get our hands dirty, take the necessary steps to attain
required expertise in building the A-arm in the SC Racing laboratory using carbon fiber and
take control of the Formula SAE racing track.
References:
[1] Reza N. Jazar (2008). Vehicle Dynamics: Theory and Applications. Spring. p. 455.
Retrieved 2012-06-24.
[2] http://www.everyday-wisdom.com/formula-one-race-car.html
[3] W.J. Cantwell, J Morton (1991). "The impact resistance of composite materials – a
review". Composites 22 (5): 347–62. doi:10.1016/0010-4361(91)90549-V
[4] Baumgart F. (2000). "Stiffness--an unknown world of mechanical science?". Injury
(Elsevier) 31. Retrieved 2012-05-04. "“Stiffness” = “Load” divided by “Deformation”"
[5] http://www.everyday-wisdom.com/formula-one-race-car.html
[6] Roman Hillermeier, Tareq Hasson, Lars Friedrich, Cedric Ball. "Advanced
Thermosetting Resin
[7] http://students.sae.org/competitions/formulaseries/west/eventguide.pdf
[8] http://www.zoltek.com/carbonfiber/