Student Car

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

806 A Mihailidis, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis

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

The design of a Formula Student race car 807


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



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



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



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



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)



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



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



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



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



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.

REFERENCES

1 Formula SAE rules, SAE International, Warrendale,Pennsylvania, USA, 2007, available from http://www.sae.org.

2 Puhn, F. How to make your car handle, 1976 (HPBooks, Los Angeles, California).

3 Auer, B., McCombs, J., and Odom, E. Design andoptimization of a Formula SAE frame. SAE techni-cal paper 2006-01-1009, 2006.

4 Henningsgaard, A. and Yanchar, C. Carbon fibrereinforced steel spaceframe techniques. SAE tech-nical paper 983055, 1998.

5 Smith, C. Tune to win, 1978 (Aero Publishers,Fallbrook, California).

6 Goel, V. K. and Ramji, K. Analytical predictions ofsteady state tyre characteristics. Int. J. Veh. Des.,2004, 34(3), 260–285.

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9 Bayle, P., Forissier, J. F., and Lafon, S. A new tyremodel for vehicle dynamic simulations. In Pro-ceedings of Automotive Technology International’93, 1993, pp. 193–198 (UK and International Press,Dorking, Surrey).

10 Bakker, E., Nyborg, L., and Pacejka, H. B. Tyremodelling for use in vehicle dynamic studies. SAEtechnical paper 870421, 1987.

11 Kasprzak, E. M. and Gentz, D. The Formula SAETire Testing Consortium – tire testing and datahandling. SAE technical paper 2006-01-3606, 2006.

12 Milliken, W. F. and Milliken, D. L. Race car vehicledynamics, 1996 (SAE International, Warrendale,Pennsylvania).

13 Barak, P. Magic numbers in design of suspension forpassenger cars. SAE technical paper 911921, 1991.

14 Gaffney III, E. F. and Salinas, Z. R. Introduction toFormula SAE suspension and frame design. SAEtechnical paper 971584, 1997.

Fig. 20 View of the car



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

DAAAM Symposium, Vienna, Austria, 2008, pp.853–854 (DAAM International, Vienna).

17 Shih, S. and Bowerman, W. An evaluation oftorque bias and efficiency of Torsen differential.SAE technical paper 2002-01-1046, 2002.

18 Looman, J. Zahnradgetriebe, 1995 (Springer-Verlag,Berlin).



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