The design of a Formula Student race car: a case studyA Mihailidis*, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis
Department of Mechanical Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece
The manuscript was received on 28 November 2008 and was accepted after revision for publication on 5 March 2009.
DOI: 10.1243/09544070JAUTO1080
Abstract: This paper presents the procedure followed in order to design the first FormulaStudent race car of the Aristotle University of Thessaloniki, Greece. Despite the restrictionsimposed by the Formula SAE rules, the designer has a broad range of freedom in creativity andinnovativeness. The design concept of the main vehicle parts, such as the frame and thesuspension, is described and the design objectives and assumptions are analysed. The paperalso focuses on several new features regarding the suspension adjustments, the steeringsystem, and the engine modifications. Following this procedure, it was made possible to build acompetitive and reliable car in a period of just 9 months.
Keywords: Formula Student, Formula SAE, tubular space frame, suspension design,drivetrain, engine
1 INTRODUCTION
Formula Student (or Formula SAE (F-SAE)) is a
worldwide university competition, organized by the
Society of Automotive Engineers (SAE), which en-
courages university teams to design, build, and
compete with a Formula-style race car. To partici-
pate in the competition the vehicles must comply
with the F-SAE’s strict rules [1]. The competition is
split into static and dynamic events. Static events
include vehicle presentation, cost, and design ana-
lysis, while dynamic events include four racing con-
tests: acceleration, skid pad, autocross, and finally
the endurance and fuel economy event. Common
characteristics of all dynamic events are the very
tight corners, the intense speed fluctuations, and
the need for good vehicle handling. More informa-
tion about the competition can be found in the F-SAE
rules [1].
This paper presents the design procedure that
was followed in order to design and build a fully
operational and high-performance single-seater race
car. It was decided that the car should not only fulfil
the requirements set by SAE but also should be
durable and easy to adjust over a wide range. This
decision was based on the intention to use the car as
a running test bench that should allow for on-track
measurements as well as for suspension and motor
set-up evaluation. Data from on-track experiments
will serve as a valuable feedback for future similar
efforts. In addition, the paper focuses on the new
features introduced and the implementation of their
design. They include the fully adjustable suspension
mechanism, the steering system, the spherical joint
mounts, the fuel tank, and the intake manifold.
Following this procedure the first Formula
Student race car of the Aristotle University of
Thessaloniki, Greece, was designed and built. The
vehicle participated in two competitions and proved
to be reliable, finishing all dynamic events with good
scores.
In the following, the design of the frame is
described first (section 2) because it is clearly one
of the most important parts of a race vehicle, as
it affects strongly its drivability and performance.
Moreover, once manufactured, major modifications
are usually difficult and expensive. However, it is not
the first task of the overall design procedure shown
in Fig. 1. Several decisions regarding the overall
dimensions, the suspension, and steering system as
well as the powertrain have to be met first, as out-
lined in sections 3 and 4 respectively. Further, it can
be finalized only after the design of the subsystems.
*Corresponding author: Department of Mechanical Engineering,
Aristotle University of Thessaloniki, University Campus, Thessa-
loniki, 54124, Greece.
email: [email protected]
CASE STUDY 805
JAUTO1080 F IMechE 2009 Proc. IMechE Vol. 223 Part D: J. Automobile Engineering
2 FRAME
The frame design has to fulfil several contradicting
design requirements.
1. The frame has to be light but also safe and stiff.
High torsional stiffness has a great impact on the
handling of the car [2, 3] because it affects
unfavourably the vertical load distribution. It also
reduces the torsional springing. The torsional
stiffness of the frame should be at least ten times
greater than the roll stiffness of the suspension
[2].
2. The frame must be compact but should also allow
for easy inspection, servicing, and replacement of
all main parts of the vehicle.
The first decision that has to be taken concerns
the type of frame. It is known that monocoques
made from carbon composites are lighter and stiffer
than tubular space frames [4]. However, space
frames are easier to produce and less costly. Fur-
thermore, they are easier to inspect, to modify, and
even to repair in the case of an accident. There-
fore, it was decided to design the frame from steel
tubes. Next, the cross-section of the tubes has to be
chosen. Even though rectangular tubes are easier
to join than circular ones, it was decided to use cir-
cular tubes because they offer a much higher
stiffness-to-weight ratio.
Besides the aforementioned design requirements,
many parameters have to be determined and kept in
mind in order to design a race frame successfully.
The most important are as follows:
(a) the overall vehicle dimensions as well as the
suspension type and geometry, so that the
points where loads act are known; they are
determined according to the suspension design
as described in section 3;
(b) the engine and drivetrain components, which
are going to be used; it is important to decide
how they should be integrated in the frame and
where the resulting forces and moments will act
(see section 4);
(c) human factors, regarding ergonomics and con-
trols; particular attention should be given to the
seat-belt attachment points, the pedals, and the
head cushion;
(d) the F-SAE rules [1], and especially those con-
cerning the driver’s safety, i.e. front and side
impact protection as well as main and front hoop.
In the current case, the positions of the seat-belt
attachment points were set according to the F-SAE
rules [1]; the brake pedal was designed to withstand
1500 N, which is the maximum force that the driver
can exert in panic situations; and finally the head
cushion was made from Ethafoam and verified to
withstand 1000 N applied rearwards. Regarding the
seating position of the driver the following dim-
ensions were chosen: seat height, 80 mm; design
seatback angle relative to vertical, 35u; steering wheel
height, 440 mm; horizontal distance from the steer-
ing wheel to the ball of the foot, 560 mm; horizontal
distance from the steering wheel to the H-point,
330 mm. These dimensions resulted in a comfortable
driving position for drivers about 175 cm tall. In
Fig. 1 Overall design procedure
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Proc. IMechE Vol. 223 Part D: J. Automobile Engineering JAUTO1080 F IMechE 2009
order to obtain a comfortable driving position for
taller drivers either the pedals or the steering wheel
should be made adjustable.
All the above were embedded in a three-dimen-
sional computer-aided design model, developed in
Autodesk’s Inventor. The space frame was designed
using the previously determined load-receiving
points as nodes. This rule has been followed
wherever possible in order to avoid bending of the
frame members. The nodes were then connected by
tubes. Additional frame members were added in
order to form triangles, since they are much stiffer
than rectangles.
In order to verify the strength and to choose the
proper dimensions of the frame members, calcula-
tions were carried out using a simple finite element
beam model (shown in Fig. 2(a)) that allows for easy
and rapid design changes. It should be noted that
suspension and powertrain elements such as wish-
bones, pushbars and springs, wheel uprights, and
anti-roll bars as well as engine and differential
elements were included in this model, in order to
obtain the correct loads on the frame. Shell element
models were used to approach parts with compli-
cated geometries such as the suspension mounts
(Fig. 2(b)). Pre- and post-processing were carried out
in BETA CAE System’s ANSA and mETA respectively,
while MSC’s NASTRAN was used as the solver. The
analysis included extreme load conditions to ensure
that the space frame fulfils the main design goals:
(a) cornering with 1.5 g;
(b) simultaneous cornering with 1.5 g and braking
with 2 g;
(c) accelerating with 2 g;
(d) braking with 2 g;
(e) braking with 2 g and failure of one of the two
available brake circuits.
The above boundary conditions are not set by the
F-SAE rules, but they were chosen on the basis of
preliminary calculations assuming a tyre friction
coefficient m 5 2 and sufficient engine torque to spin
the tractive wheels. However, measurements carried
out on the built car showed that the above values are
rather overestimated. In particular, the maximum
lateral acceleration was 1.3 g, the longitudinal accel-
eration was 1 g, and the braking deceleration was 2 g.
The final space frame is shown in Fig. 3. The frame
has a calculated torsional stiffness of about 3450
N m/deg, which is almost 14 times greater than the
roll stiffness of the suspension. The durability of the
frame must be sufficient to withstand the necessary
tests and the races. Taking into account that
Formula Student cars are allowed to participate in
races that take place during 1 year, many of these are
designed for a limited fatigue life, in order to save
weight. However, the current frame was designed
below the endurance limit, i.e. for theoretically
infinite life, since it was decided to use the car for
tests and training of the drivers even after the racing
Fig. 2 (a) The frame beam model; (b) shell element model, and finite element analysis results ofsuspension mounts
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JAUTO1080 F IMechE 2009 Proc. IMechE Vol. 223 Part D: J. Automobile Engineering
period. This is the main reason for the relatively high
net frame mass of 35 kg. Some details, which further
increased the mass, are shown in Fig. 3. The front
plate 1 is supported by two rectangular tubes and is
shown in detail in view A. It completely isolates the
impact attenuator (shown in Fig. 4) from the driver’s
feet. The cross tube 2 with the seat-belt attachment
points 3 and 4 is supported by the diagonal members
5 and 6. The side impact protection structure
includes three more members 7, 8, and 9 per side
than the obligatory 10, 11, and 12. Finally, it should
be noted that the mounting plates 13 and 14 of the
lower wishbones allow for the anti-dive and anti-
squat adjustment.
Several compromises were required to keep the
centre of gravity as low as possible, such as
mounting the battery and the fuel tank as low as
possible, reducing the size of the engine oil sump,
and finally installing the driver’s seat to the already-
mentioned low position.
The impact attenuator is interchangeable and
mounted on the frame by eight screws. They are
positioned in the lateral direction as can be seen in
Fig. 4(a) for safety reasons. If a mounting screw were
in the longitudinal direction, then one of its fractures
could enter the cockpit and injure the driver in case
of an impact. According to the F-SAE rules, the
Fig. 3 The final space frame (for explanation ofnumbers, see text)
Fig. 4 (a) The impact attenuator and its mounting onto the frame; (b) detail of the shell elementmesh; (c), (d) results of the finite element analysis
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Proc. IMechE Vol. 223 Part D: J. Automobile Engineering JAUTO1080 F IMechE 2009
impact attenuator must be designed so that, when a
vehicle with a total mass of 300 kg runs into a solid
non-yielding impact barrier with a velocity of 7 m/s,
the average deceleration does not exceed 20 g. The
current design was evaluated by the finite element
method with ANSA as the pre-processor and LS-
DYNA as the solver; the results are shown in Figs 4(b),
(c), and (d). The mean deceleration at a crash with a
velocity of 7 m/s was calculated as 15.5 g.
3 SUSPENSION
The main design requirements of the suspension
design of a Formula Student race car are the following:
(a) the ability to keep all four wheels in contact with
the ground at the correct angles in order to
exploit the maximum tractive force of the tyres;
(b) the ability to have many adjustments, since
different races often require alternative set-ups,
and in this case it was decided that the suspen-
sion design should include the following adjust-
ments: camber angles, anti-roll bar stiffness, front
and rear anti-features, as well as steering angles;
(c) optimal vehicle manoeuvrability;
(d) compliance with F-SAE rules.
The following sections describe how these objec-
tives were met.
3.1 Overall dimensions
The track and the wheelbase of the car are the first
parameters to be defined. According to the F-SAE
rules the wheelbase must be at least 1525 mm and
the narrower track must be no less than 75 per cent
of the wider track. In general, race cars with short
wheelbase and wide tracks are less stable in straight
line. In contrast, they are more manoeuvrable and
allow for higher cornering speeds [5]. This type of
handling performance is suitable for the Formula
Student competition because the circuits consist of
many small-radius (4.5 m minimum) corners, while
straight lines are limited in number and length. The
front track width was chosen to be 1297 mm, the rear
1250 mm, and the wheelbase length 1650 mm, so as
to ensure easy accessibility to all main car compo-
nents and to improve space availability.
3.2 Wheels and tyres
After the track width and wheelbase were defined,
the next step was to choose the appropriate tyre size
and type. According to F-SAE rules, only 10 in and
13 in wheel sizes are allowed. Eventually, 13 in
wheels were chosen because they provide more
space for the brake discs and callipers.
Tyre behaviour is very complex and depends
strongly on road surface, inflation pressure, oper-
ation temperature, speed, normal force, camber
angle, and other parameters. Many analytical mod-
els have been developed in order to predict the tyre’s
behaviour [6–10]. However, the implementation of
these models requires the knowledge of numerous
parameters, which are usually either not available or
difficult to determine. For this reason, tyre data
given by the Calspan Corp. were used [11]. One of
the most important characteristics of a tyre is the
lateral force–slip angle diagram because it describes
the way that the tyre will react in cornering. In Fig. 5,
diagrams of two typical Formula Student tyres are
shown. Tyre D is a diagonal tyre, and tyre R a radial
tyre. The need for a wide range of camber angle
adjustments is evident, especially if tyre D is used.
3.3 Type of suspension
Unequal-length double wishbones with push rod
actuators were chosen for the front and the rear
suspension of the vehicle, as presented in Fig. 6. This
type of independent suspension is typical for
Formula-type race cars for the following reasons [5].
1. It allows for four-wheel independence.
2. The linkages are loaded just in tension or
compression; there are no bending moments.
3. The total unsprung mass is reduced.
4. Convenient adjustment of camber angle and anti-
features is possible.
5. Progressive wheel rate can be achieved by prop-
erly designing the bell cranks.
3.4 Suspension geometry
The placement of the roll centres plays an important
role in the vehicle’s behaviour because it influences
the way that the camber angle changes during
cornering [5, 12, 13]. They also define the roll axis
around which the frame pivots when it is laterally
loaded. If the roll centres are close to the ground,
excessive roll occurs which may require too high
wheel rates. Otherwise, if they are close to the centre
of gravity, roll is minimized. This helps to reduce the
anti-roll bar stiffness and the wheel rate but on the
other side the frame receives jacking forces during
cornering [5, 12–15]. When defining the attachment
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JAUTO1080 F IMechE 2009 Proc. IMechE Vol. 223 Part D: J. Automobile Engineering
points of the wishbones, care should be taken to
avoid excessive roll centre migration. In the current
case, the front and rear roll centres were set at 36 per
cent and 40 per cent of the centre of gravity height
above ground. Their vertical migration is negligible
and the lateral migration is about 80 mm.
Pitching motion is even more disturbing than
bounce motion [13]. This is why an ideal suspension
could be designed for 100 per cent anti-dive and
anti-squat in order to eliminate pitch rotation during
braking and accelerating. However, ‘anti’ features
force the suspension to appear stiffer and less
sensitive. During high longitudinal accelerations the
tyre forces are transmitted directly to the frame, by-
passing the springs and the absorbers. Therefore,
the suspension remains undeformed in contrast with
the tyres. Their compliance becomes excessive and
severe tramp may occur [5, 13]. In order to optimize
the vehicle’s behaviour under acceleration alter-
nations, adjustable anti-dive and anti-squat are im-
plemented. Both front and rear lower wishbones
have four tune-up positions varying from 20 per cent
to 84 per cent anti-dive and from 30 per cent to 100
per cent anti-squat, which can be easily adjusted by
altering the frame mounting positions, as shown in
detail A in Fig. 7.
The desirable range for the camber angle alter-
nations was estimated from the tyre’s performance
curves (Fig. 5) and it was used to determine the
lower and upper wishbone lengths. Depending on
the tyres used, the static camber can be easily
changed by means of different spacers at the wish-
bone mountings, as shown in detail B in Fig. 7.
As mentioned earlier, the bell crank geometry
affects the wheel rates. By altering the angles q1 and
q2 and radii l1 and l2 of the bell crank (Fig. 8(a)), the
ride rates can be adapted to different tracks and
driving styles. The bell cranks were designed to give
a progressive wheel rate, as shown in Fig. 9, mainly
at the front in order to react better in low road
irregularities [12]. The bell cranks are supported by
Fig. 5 (a) Tyre D and (b) tyre R lateral force–slip anglediagrams
Fig. 6 (a) Front and (b) rear suspension
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Proc. IMechE Vol. 223 Part D: J. Automobile Engineering JAUTO1080 F IMechE 2009
two preloaded angular ball bearings in an O
arrangement so as to be clearance free. A section
view of the mounting is shown in Fig. 8(b).
The choice of the appropriate diameter of the anti-
roll bars depends on the circuit conditions and the
driver preferences. Therefore, they were designed to
be easily interchangeable.
The caster angle specifies the mechanical trail of
the wheels and generates the self-steering effect. The
caster and kingpin inclination influence the steer-
camber characteristics. These angles were chosen so
that, during cornering, the outside wheel has a more
negative camber, while the inner has a more positive
camber. In the current case these angles were
chosen to be 6u and 14.5u respectively. The steer-
camber characteristics are shown in Fig. 10 for two
static camber adjustments. For example, if the static
camber is set at 0u, when the car turns in a tight
Fig. 7 View of suspension adjustments
Fig. 8 (a) Top view of the front bell crank with thepush rod and the shock; (b) section view of thebell crank mount
Fig. 9 Front- and rear-wheel rates
Fig. 10 Steer-camber characteristics for all anti-diveadjustments and for two static camber adjust-ments
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corner the camber angle of the outer wheel is 21.5uand that of the inner wheel is +5u. It should be noted
that anti-dive has negligible effect on the camber
angle change.
In all suspension joints, clearance-free spherical
bearings were used. They have to be easy to replace
and mounted clearance free. Figure 11 shows the
design of a bearing mount which fulfils these
requirements. It was proven to be compact, light,
reliable, and cost effective [16].
Figure 12 shows the design of the front uprights.
They must be as light as possible, because their mass
is unsprung, and stiff enough to hold the forces from
the tyres without altering the suspension geometry.
The pushrod 2 is mounted straight on the upright 1
with a spherical bearing B and not at the lower
wishbone 3, as is the common practice. In this way,
bending of the lower wishbone is avoided and the
suspension linkages are loaded only in tension or
compression. The spherical joints A, B, and C lie on
the kingpin axis.
3.5 Steering geometry
In order to provide the proper steering angles while
maintaining minimum bump steering and to gain
adjustability, the steering mechanism shown in
Fig. 13 was developed. It consists of a rocker 1
which transmits the axial motion of the rack 2 to the
tie rod 3 via the auxiliary rod 4.
During cornering, the outside wheels receive a
much greater normal force than the inside because
of the lateral weight transfer. Their slip angles define
mainly the actual centre of the turn O. In the case
of Ackermann steering the resulting slip angles afi
and ari of the inner wheels will be greater than
required (Fig. 14). The result is that the car could
slow down because of the drag of the inner wheels.
Moreover, their temperature and wear would rise. In
order to avoid these phenomena the inner wheel
should be steered at a smaller angle. Therefore, by
mounting the rocker 1 in one of the alternative
positions A, B, and C shown in Figs 13(a) and (b), the
steering geometry can be adapted to the racing
conditions. In Fig. 13(c) the steered wheel angles are
presented for the three alternative adjustments. The
position of the tie rod on the upright is defined so
Fig. 11 Spherical bearing mount design: 1, carryingpart; 2, carrying ring; 3, deformed lips; 4, outerring; 5, inner ring; 6, spacers; 7, U-holder;A1, A2 and A3, A4, frictional-force-transmit-ting surfaces
Fig. 12 (a) Front wheel upright; (b) finite element results when braking with 2 g (for explanation,see text)
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Proc. IMechE Vol. 223 Part D: J. Automobile Engineering JAUTO1080 F IMechE 2009
that the bump steering is minimized. In this case a
bump steering of only 0.03u was achieved. Anti-dive
adjustments also affect the bump steering. There-
fore, the tie-rod mounting height on the rockers was
designed to be adjustable to ensure that bump
steering remains low for every anti-dive setting as
shown in detail C in Fig. 7.
The rack and pinion steering was designed to
provide zero clearance as shown in Fig. 15. The rack
1 is driven by the two helical pinions 2. Elimination
of clearance is achieved by axially preloading the
Belleville springs 3 between the two pinions by
means of the nut 4. In this way the left flanks of the
first pinion and the right flanks of the other are
pressed permanently on the rack.
4 POWERTRAIN
A 2005 Honda CBR 600RR motorcycle engine (engine
type PC37E) was chosen. The original equipment
manufacturer (OEM) configuration of the engine
provides 61.8 N m torque output at 11 000 r/min and
79.6 kW power output at 13 000 r/min.
In order to install this engine to a Formula-type
car, several problems need to be addressed. The
most important of these concern the following:
(a) the mounting of the engine in the frame;
(b) the engine lubrication during cornering;
(c) the installation of a new fuel tank and fuelling
system;
(d) the new intake and exhaust manifold design
according to F-SAE regulations.
Starting from the mounting, there are two possi-
bilities: the engine block can be used as part of the
frame as is done in Formula-1 cars or, alternatively,
the engine can be mounted in the frame in a way
that does not allow the block to receive any forces or
moments. The latter approach was followed in the
current case, since it ensures that the deformations
of the engine block remain in the range that its
manufacturer has foreseen. The engine is attached to
the frame at eight points using rubber silent blocks.
This ensures not only that the deformations of the
frame do not load the engine block but also that
vibrations are partially isolated from the frame.
Regarding engine lubrication the following problem
can be experienced owing to the original use of the
engine in a motorcycle. During cornering, the engine
of a car remains almost upright, unlike the engine of
a motorcycle that leans. Therefore, the lubricant
drifts towards the sides of the sump, and the
lubricant flow in the pump may be disrupted. In
order to ensure proper lubrication, separators were
added in the oil sump. Furthermore, its height was
reduced in order to allow for a lower mounting of the
engine. This design was chosen instead of a dry
sump because it is cheaper, easier to manufacture,
and lighter than the dry sump option since no
additional mechanical parts are required.
As concerns the fuelling system, selective laser
sintering (SLS) technology was used for the produc-
tion of the fuel tank. In Fig. 16 a detailed view of
the fuel tank is presented. The overall weight and
number of parts are significantly reduced because
SLS provides the ability to create complex and
compact geometric forms out of plastic material.
Several modifications had to be made to the
engine intake manifold to meet the F-SAE regu-
Fig. 13 Adjustable steering geometry in (a) full Ack-ermann and (b) parallel set-up. (c) Angles ofsteered wheels for the alternative steeringgeometries
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lations. According to these regulations, a 20 mm
restrictor must be placed in the intake manifold in a
way that all intake airflow passes through it. In
addition, a single throttle must be used and placed
before the restrictor. These requirements signifi-
cantly affect engine operation and performance.
Furthermore, the engine was originally designed to
deliver its nominal power and torque at relatively
high speeds (above 11 000 r/min). The presence of a
restrictor and the racing conditions of the F-SAE
competitions call for lower-engine-speed driving.
Therefore, new intake and exhaust manifolds were
designed, aimed at achieving the highest possible
torque and power output in the 7000–9000 r/min
operating range. The new intake manifold was
manufactured by SLS, the exhaust manifold by
welded stainless steel tubes. In order to compen-
Fig. 14 Steering angles
Fig. 15 Rack and pinion steering (for explanation of numbers, see text)
Fig. 16 Fuel tank: 1, fuel pump mount; 2, main com-partment; 3, secondary compartment used asoverflow tank; 4, fuel inlet; 5, overflow inlet;6, 7, air venting tubes
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Proc. IMechE Vol. 223 Part D: J. Automobile Engineering JAUTO1080 F IMechE 2009
sate for the new intake and exhaust systems and to
achieve high engine performance, a new engine cali-
bration was necessary. A programmable electronic
control unit (ECU) by Motec was used in order to
introduce the new engine control strategy in line
with the aforementioned modifications. Finally, a
new cooling system was designed in order to provide
adequate cooling under low-average-speed, high-
power-output conditions, similar to those encoun-
tered in Formula Student races, and to fit in the frame
without compromising the vehicle weight balance.
It was decided that the engine should be config-
ured with respect to the acceleration performance
rather than the top speed, because the average race
speed is limited to approximately 60–70 km/h. Since
the restrictor causes a significant drop of the engine
power output at high engine speeds (over 11 000
r/min), operation is optimized to the 7000–9000 r/min
range. To save experimental time, the intake and
exhaust manifolds were initially studied and opti-
mized using computer simulation. The engine was
modelled in Gamma Technologies’ GT-POWER, and
the intake and exhaust runner lengths, the air-box
volume, and the restrictor–diffuser system were
studied to maximize the volumetric efficiency in
the predetermined speed range. Figure 17 shows the
intake manifold. Two sets of intake runners were
foreseen, in order to provide a different maximum
torque output curve according to the demands of each
race track. The air filter is placed in the air box to assist
the diffusion of the incoming air. Appropriate engine
calibration was conducted for each intake configura-
tion. The resulting torque and power curves are shown
in Fig. 18.
The new ECU was programmed using an engine
dynamometer to optimize the power output and fuel
efficiency by tuning parameters such as the spark
advance, fuel injection timing, and lambda value.
The aim was not only to have an efficient and
competitive engine but also to provide the ability of
using different control strategies according to the
requirements of each event. Thus, a leaner air–fuel
mixture is used in the endurance and fuel economy
event to minimize consumption, and a richer mixture
for maximizing power during the autocross and the
acceleration events.
The self-contained gearbox of the engine was
used. Engine power is transmitted to the rear wheels
by a chain drive and a differential. The gears are
shifted by an electropneumatic quick-shift mechan-
ism mounted in the rear of the driver’s seat. The
quick shift contains an onboard air compressor and
an adequate pressure accumulator so as to allow an
unlimited number of gear shifts. Also, it is coupled
with the engine ECU and cuts off the ignition for
40 ms during gear shifting. The driver can easily and
rapidly shift the gears by pressing buttons mounted
on the steering wheel. The final transmission ratio of
the chain drive is 43/12 5 3.583 in order to enhance
the acceleration performance of the car.
Fig. 17 Intake manifold and runners Fig. 18 Output torque and power curves achieved
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A Torsen type II differential (Fig. 19(a)) was
chosen because it gives better drivability at the exit
of the corner and better traction during straight-line
acceleration. Its torque bias is affected by the initial
preloading, the input torque, and the friction co-
efficient between the faces of the planetary gears
and the cage of the differential [17, 18].
Regarding the mounting of the differential, it had
to be decided whether to mount it on the engine or
directly in the frame. In the first case the trans-
mission forces do not load the frame. However, in
the presented design it was chosen to mount the
differential in the frame using two L-shaped arms
1, as shown in Fig. 19(b). In this way the engine
and the differential can be dismounted or changed
independently from each other.
5 RESULTS
The design procedure described above can be
summarized as follows. Given the F-SAE rules, the
human factors regarding ergonomics and controls,
and the required safety, the overall dimensions, and
the engine are decided first. Then, the wheels and
tyres, the type of the suspension and its geometry,
and the steering geometry have to be chosen. An
initial frame design may follow. It should be
finalized after the design of the major car subsys-
tems. It is important initially to set clearly the design
objectives of each subsystem. The bodywork is the
last step to complete the design. This procedure in-
cludes of course much iteration because no explicit
answers can be given to the complex questions that
Fig. 19 (a) Magnified view of the differential. (b), (c) Chain pre-tension and differential mount:2, chain; 3, bolt; 4, Belleville springs
816 A Mihailidis, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis
Proc. IMechE Vol. 223 Part D: J. Automobile Engineering JAUTO1080 F IMechE 2009
arise during the development. Although Formula
Student race cars and passenger cars are totally
different, the presented design procedure can be
adopted to speed up the development, especially in
cases where the design of a completely new model
is required. Figure 20 shows the completed car.
It took part in two Formula Student contests, in
Fiorano Mondenese, Italy, in September 2007, and in
Silverstone, England, in July 2008, where it achieved
the following results. In the acceleration event the
car needed just 4.405 s to cover 75 m, whereas the
competitor finishing first needed 3.997 s, and the
competitor finishing last, 7.5 s. In the skid pad the
best time of the presented car was 5.471 s, whereas
the best time was 5.02 s and the worst 10.277 s. The
tight course of the autocross event was covered in
61.65 s, while the fastest car needed 9.7 s less and the
slowest 67.66 s more. The 22 km of the endurance
event was covered in 1465.96 s. The fastest car
needed 227.41 s less and the slowest 456.75 s more.
Taking into account that, from the 78 competing
cars, only 24 managed to complete the endurance
event, the vehicle proved to be not only competitive
but also reliable.
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Fig. 20 View of the car
The design of a Formula Student race car 817
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15 Reimpell, J. and Stoll, H. The automotive chassis:engineering principles, 1996 (SAE International,Warrendale, Pennsylvania).
16 Mihailidis, A., Pupaza, C., Nerantzis, I., andKaraoglanidis, G. Modelling and simulation of aspherical bearing mount. In Annals of DAAAM for2008 and Proceedings of the 19th International
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818 A Mihailidis, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis
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