Report Example - Car Suspension Design

MECHANICAL ENGINEERING Institut Teknologi Bandung

GROUND VEHICLE COURSE FINAL REPORT i

REDESIGN AND CALCULATION OF

BRISTOL FIGHTER CAR’S

SUSPENSION SYSTEM

FINAL REPORT OF

THE GROUND VEHICLE COURSE

By :

Group 4

Indria Herman(13102108)

Yudha Azali(13102117)

Robin(13103085)

MECHANICAL ENGINEERING

ITB

2007


GROUND VEHICLE COURSE FINAL REPORT ii

CONTENTS

CONTENTS ...................................................................................................................ii

CHAPTER I INTRODUCTION ..................................................................................1

CHAPTER II BASIC THEORY ..................................................................................2

CHAPTER III BRISTOL FIGHTER CAR’S DATA ................................................8

3.1 Performance......................................................................................................9

3.2 Chassis, structure and safety.............................................................................10

3.3 Packaging..........................................................................................................10

3.4 Interior ..............................................................................................................11

3.5 Handling and Roadholding ...............................................................................11

3.6 Steering .............................................................................................................12

3.7 Brake.................................................................................................................12

3.8 Additional Information .....................................................................................13

CHAPTER IV CALCULATION .................................................................................14

CHAPTER V RESUME................................................................................................22

REFERENCES ..............................................................................................................23


GROUND VEHICLE COURSE FINAL REPORT 1

CHAPTER I

INTRODUCTION

Ground vehicle course is optional course which should be taken by the

students who took the construction and design sub-major in Mechanical Engineering ITB.

One of the part in this course cover about ride and handling of ground vehicle. This part

describe about several considerations in order to have a comfort in riding and handling.

On covering about ride and handling of ground vehicle, suspension system is the main

system that become the basic consideration. Since suspension system has become the

most influential factor that really important, nowadays, several modification have been

implemented to have a better suspension system.

In this part of ground vehicle course the students were introduced the basic

knowledge about the definition of suspension system, the parameters that influence the

characteristics of the suspension system, and the design and calculation of suspension

system. By given about all of this material course, the students are expected to have a

more comprehension which lead to a better skill if they were work in automotif bisnis.

The most practical implementation of the suspension system theory are suspension system

in car and motorcycle.

In Order to accomplish the Ground Vehicle Course, students are divided inte

groups. Each group consist of three students. Each group should make a report about the

design calculation of a ground vehicle which they are choosen before. On this opportunity

the writers choose the Bristol Fighter car which is sports car as a ground vehicle which

suspension system will be analyzed and redesign..The information about the bristol city

car is given by searching the web.



CHAPTER II

BASIC THEORY

Suspension System Before we started about how to measure the suspension system parameters, let’s

talk about what the suspension system used to. Suspension is the term given to the system

of springs, shock absorbers and linkages that connects a vehicle to its wheels as can be

seen in Picture 1. Suspension systems serve a dual purpose - contributing to the car's

handling and braking for good active safety and driving pleasure, and keeping vehicle

occupants comfortable and reasonably well isolated from road noise, bumps, and

vibrations. The suspension also protects the vehicle itself and any cargo or luggage from

damage and wear.

Picture 1. The Arrangement of the complete suspension system

In suspension system, there are two main components that make us feel comfort in

riding a vehicle: springs and shock absorbers/dampers. In this chapter, we won’t discuss

about the types of the springs and dampers. We only talk about the properties of the

suspension system:

‐ Spring rate/stiffness



Spring rate is a major component in setting the vehicles ride height or its location

in the suspension stroke. Vehicles which carry heavy loads will often have heavier

than desired springs to compensate for the additional weight that would otherwise

collapse a vehicle to the bottom of its travel (stroke). Heavier springs are also used

in performance applications when the suspension is constantly forced to the

bottom of its stroke causing a reduction in the useful amount of suspension travel

which may lead to harsh bottoming. This may vary with deflection. For active

suspensions, it may depend on other things. The softer the springs, the more

important the other requirements are. Spring rate is often a compromise between

comfort and handling, but when other things are compromised instead, as in the

1960s Lotus Elan, both may be achieved.

‐ Damping

Damping is the control of motion or oscillation, as seen with the use of hydraulic

gates and valves in a vehicles shock absorber. This may also vary, intentionally or

unintentionally. Like spring rate, the optimal damping for comfort may be less

than for control. Damping controls the travel speed and resistance of the vehicles

suspension. An un-damped car will oscillate up and down. With proper damping

levels, the car will settle back to a normal state in a minimal amount of time. Most

damping in modern vehicles can be controlled by increasing or decreasing the

resistance to fluid flow in the shock absorber.

Measurement On this assignment, we are using formulas from the book Fundamentals of

Vehicle Dynamics by T. D. Gillespie and The Shock Absorber Handbook by J. C. Dixon

to calculate the spring stiffness and damping characteristic of a car. From these books, we

have received so much information about how to measure the spring stiffness and

damping characteristic; the parameters; the assumption that we have to make; and the data

that we must collect first before doing the calculation.

To do this calculation; first of all, we must know about total weight of the vehicle

including the passengers and their luggage that might be able to put on the car. For

ground vehicle, the standard weight of one passenger is about 68 kilos with 7 kilos of



luggage (for car). Next is we must know about the wheelbase of the car and the location

of the center of gravity (CG). From this information, we could measure the mass that

being distributed on the front wheels and the rear wheels. We could also measure the

distance between the center of gravity to the front and rear wheels. All of this information

is the main information that we must have in order to do this calculation.

After received all of the information above, we should take an assumption about

the natural frequency that we wanted to appear in our suspension system design. Usually

we took the value about 1-1.5 Hz (human comfort zone) for the passenger car. From the

natural frequency that we have chosen, we could measure the spring stiffness by using

this formula:

mfk n24π=

where : k = spring stiffness/rate (N/m)

fn = natural frequency (Hz)

m = sprung mass (kg)

We could start this calculation from the front or from the rear wheels and then calculate

the others based on Olley’s criteria.

Olley’s Criteria The Olley’s criteria are:

1. The front suspension should have a 30% lower ride rate than the rear suspension,

or the spring center should be at least 6.5% of the wheelbase behind the CG.The

geometry of the car can be seen in picture 2. Although this does not explicitly

determine the front and rear natural frequencies, since the front-rear weight

distribution on passenger cars is close to 50-50, it will generally assure that the

rear frequency is greater than the front. The formula that related to this criteria is:

ab

kk

r

f

44.11

≅

where : kf = front spring stiffness (N/m)

kr = rear spring stiffness (N/m)



a = distance between front suspension and CG (m)

b = distance between rear suspension and CG (m)

Picture 2. Geometry of the car

2. The pitch and bounce frequencies should be less than 1.2 times the pitch

frequency. For higher ratios, “interference kicks” resulting from the superposition

of the two motions are likely. In general, this condition will be met for modern

cars because the dynamic index is near unity with the wheels located near the

forward and rearward extremes of the chassis.

2.1<pitch

bounce

ff

Pitch is an angular motion of the car body with the center of rotation located

between the wheelbases; while center of rotation of bounce located outside the

wheelbase. This means that bounce is more likely a vertical motion; especially

when the center of rotation located far away in front/rear of the car.

In order to fulfill these criteria, we should do some earlier calculation:

( )( )( )

Gyration of

/

/

/

222

radiusMI

k

MkbKaK

MaKbK

MKK

y

rf

fr

rf

→=

+=

−=

+=

γ

β

α

Radius of Gyration could be measure using another calculation; that is:

baDIk ..2 =

where : k = radius of Gyration



a = front-CG

b = rear-CG

DI = dynamic index (1.1 – 1.2)

M = total mass

To calculate the value of pitch and bounce frequency, we are using the formulas

below:

( ) ( )

( ) ( ) 2222

2221

/4/2

/4/2

k

k

βγαγαω

βγαγαω

+−−+

=

+−++

=

Where the value of the frequency is:

πω2

=f

3. Neither frequency should be greater than 1.3 Hz, which means that the effective

static deflection of the vehicle should exceed roughly 6 inches.

4. The roll frequency should be approximately equal to the pitch and bounce

frequencies. In order to minimize roll vibrations, the natural frequency in roll

needs to be low just as for the bounce and pitch modes.

Damping Coefficient Next thing that we should do is to calculate the value of the damper. The damping

coefficient could be determined just using a simple formula:

kmc

2=ζ

hence :

kmc ζ2=

But before we calculate the value of the damping coefficient, we must first check the ride-

handling parameter below:



designdcompromizefoptimizedhandlingf

optimizedridefff

RH

RH

RH

RH

−⇒−=−⇒=

−⇒=

=

75.125.121

23 ζ

where : fRH = ride-handling parameter

f = natural frequency of the suspension system

ζ = damping ratio

ζ = 0.2 – 0.4 → passenger car

ζ = 0.4 – 1.0 → competition car

The value of ζ (damping ratio) can be assumed depending on what kind of car that we

want to design.

Damping Force Characteristic Damping force characteristic described about how many forces that can be

absorbed by the damper in certain condition. To design this characteristic, we must

calculate the damping force in certain speed of the piston (inside the damper) with certain

tension/compression force ratio (usually between 50/50 – 80/20). Therefore, we use the

formula below:

VkmF ×= ζ

where : F = tension or compression force

V = piston velocity

The basic standard of damping characteristic is by calculated the tension and compression

forces at the velocity of the piston 0.05, 0.1, 0.3, and 0.6 m/s (both tension and

compression) with tension/compression force ratio between 50/50 – 80/20.



CHAPTER III

BRISTOL FIGHTER CAR’S DATA

In the Bristol’s car, the V-10 engine and transmission have been specially

developed to suit Bristol requirements. The rest of the vehicle has been designed to meet

the uniquely demanding requirements of a sports car capable of more than 200 miles an

hour.

Fighter is one of the very few cars ever designed where aerodynamic

efficiency has been placed ahead of all other considerations. Innovative design features

are shared with aircraft, high-speed missiles and even submarines. The teardrop form of

the passenger area ensures the lowest possible lift and drag. It also offers uninterrupted

all-round vision whilst the dramatic gullwing doors are an intelligent solution on a

sporting car to ensure easy entry and exit even in confined spaces. Supremely elegant but

with a steely hint of aggression, the Fighter is a perfect example of the beauty that

inevitably results when form exactly follows function. This superior characteristic can be

seen in picture 3.

Picture 3. Bristol fighter car’s aerodynamic design



A summary about the technical and design features of Bristol Fighter car will

be explained bellow.

3.1 Performance

• All-aluminium V-10 engine is unusually light and compact. Specific output of one

horsepower per pound of weight sets a new benchmark for class.

• Power output of 525 bhp increases further at very high speed due to

aerodynamically induced supercharging effect. Maximum speed approximately

210 mph.

• Excellent traction permits 0-60 mph in approximately 4 secs.

• Generous torque, high gearing and low drag ensure pleasing fuel economy. Even

our "lead-footed" factory test drivers regularly return over 20 mpg.

• 6-speed, close ratio manual gearbox allows 60 mph in first gear, 100 mph cruising

at 2,450 rpm in 6th.

• Engine produces an effortless flow of torque. Even at tickover there is 350 lb.ft

(476 Nm) available. Generous peak torque of 525 lb.ft (714 Nm) is achieved at

4,200 rpm.

Picture 4. Chassis of the Bristol car



3.2 Chassis, Structure and Safety

• Immensely strong chassis structure which can be seen in picture 4, with steel sill

boxes and cross members, honeycomb aluminium floors, aluminium torsional

bulkheads.

• Inner structure in aluminium with hand formed aluminium outer body panels to

ensure longevity.

• Carbon fibre doors and tailgate ensure maximum stiffness and contribute to a

lower centre of gravity.

• Massive steel tube rollover structure and safety cage provides advanced levels of

passenger protection in a really severe impact.

• Optional four point racing type seatbelts.

• As with expensive racing cars, Fighter is built over a steel surface plate enabling

each part to be accurately positioned in three dimensions. There is thus none of the

build up of tolerances that occur in mass produced and normal hand-built cars.

• Use of aerospace materials and design techniques trim weight to a moderate 1,475

kg (3,310 lb).

• Electronic tyre pressure monitors and alarms are a standard fitment.

3.3 Packanging

• Generous accommodation for occupants up to 6'7" tall. Ample electric adjustment

for seats and steering wheel makes all sizes comfortable.

• Boot area accessible from within and without, accommodates luggage for long

distance touring or two large golf bags.

• 23-gallon (105 litre) fuel tank gives touring range in excess of 400 miles. 28.5-

gallon (130 litre) tank is optional.

• In the event of tyre trouble a full sized spare tyre is standard so that you may

safely and conveniently continue your journey.



• Genuinely compact external dimensions make driving in traffic or on challenging

smaller roads a pleasure.

• Panoramic visibility for maximum safety and driving enjoyment.

• Turning circle rivals most city cars, 100% Ackerman steering geometry avoids

unseemly tyre scrub.

• 8" ground clearance ahead of front wheels and 6" beneath car eliminates

possibility of grounding over speed bumps or on steep driveways.

• Sets new standards for space utilisation in fast cars.

3.4 Interior

• Modern and efficient in layout, stylish and elegant in appearance.

• Extensive aircraft style instrumentation includes oil temperature and pressure, fuel

system pressure, outside air temperature and engine hours displays.

• Compact overhead aircraft-style console houses gauges and switch panel.

• Special attention to tactile quality of switchgear.

• Deeply bolstered armchair-type seats provide cosseting comfort with excellent

lateral support in fast driving.

• Excellent oddment space and access to luggage area from within.

• Latest technology photo luminescent switch panels for glare-free operation at

night.

• Flawless soft hand stitched leather covers the interior surfaces.

• Leather edge-bound Wilton carpeting with thick sound proofing layers.

• Stylish gullwing doors make entry and exit a pleasure, especially in confined

spaces.

3.5 Handling and Roadholding

• Front mid-engine design gives low polar moment of inertia for agile handling

response.

• 52% of weight on rear wheels gives superior traction and braking performance.



• Unusually low centre of gravity minimises weight transfer and improves

roadholding.

• Fully independent double-wishbone suspension with coil-over racing type

dampers for exceptional comfort and control.

• Steering and suspension set entirely new standards for geometric precision and

accuracy.

• Fuel tank mounted around the centre of gravity to eliminate handling changes as

fuel load varies.

• Wide 285/40 x 18" tyres front and rear on 10" rims generate superb adhesion.

Rated for speeds over 200 mph.

• Every car individually set up to exact specification including adjusting to exact

corner weights.

• Adjustable electronic traction control fitted as standard.

3.6 Steering

• Rack and pinion with rapid 2.7 turns lock to lock.

• Power assistance tailored to owner's individual preference.

• Electric 4-way adjustable steering column. Unique steering wheel design enhances

instrument visibility.

• Steering mechanism optimised for accuracy and correct feedback.

• Genuine feel of the road retained in slippery conditions.

3.7 Brakes

• Front 6-piston callipers with 343 x 32 mm ventilated discs.

• Rear 4-piston callipers with 343 x 26 mm ventilated discs.

• Careful thermodynamic design ensures freedom from fade in hard use.

• Moderate servo assistance ensures progressive response and correct pedal feel.

• Powerful separate emergency/parking brake callipers on rear.

• All Bristol Cars are subject to continuous development and this specification can

change and may differ from that outlined above.



3.8 Additional Information

• FIGHTER 'S' (optional) Max power 628/660 bhp* at 5900 rpm. Max torque 580

lb.ft 3900 rpm.

* Horsepower increases at high speed due to aerodynamic overpressure in inlet

system

• Drivetrain - 6-speed manual or optional 4-speed automatic. Final drive 3.07:1 with

limited slip function.

• Structure - Massively strong steel and aluminium platform chassis. Steel rollover

safety cage. Aluminium exterior panels fanned by hand. Carbon fibre doors and

tailgate.

• Suspension - Front: unequal length wishbones with concentric spring/damper

units. Anti-roll bar. Anti dive geometry. Rear: unequal length wishbones with

supplementary toe control arm and concentric spring/damper units. Anti-roll bar.

Anti-squat geometry.

• brakes - Front: ventilated disc with six piston calipers. Rear: ventilated disc with

four piston calipers. Servo assistance.

• wheels - 18 X 10" forged aluminium

• tyres - Front and Rear: 285/40 X 18. Spare: full size wheel and tyre. Space saver

optional.

• Fuel Capacity : 100 litres standard, normal range 350-500 miles. 135 litres

optional range 425-650 miles.

• Dimension - Length: 4420 mm. (14'6"). Width: 1795mm. (5'10") Height:

1345mm. (4'5") Wheelbase 2750mm. (9") Front track and Rear track: 1470mm.

(4'10") Kerb Weight: 1540kg. (3450lb) Turning circle: 11.5m (37'9")



CHAPTER IV

CALCULATION

4.1 Stifness Spring Rate Calculation

Bristol Fighter Car’s Information :

• Total Sprung Mass kgmtotal 1540=→ (vehicle + 2 passenger + luggage)

• Wheel Base = 2,75 m

• totalrear mm .52,0= (gives superior traction and breaking performance)

• Maximum Torque is 580 lb.ft at 3900 rpm

Assumption :

• ζ = 0,4 ( passenger car )

• Front natural frequencies = 1 Hz

• Rear natural frequencies = 1,5 Hz

Criteria :

• Human comfort zone

natural frequency between 1-1,5 Hz

• Olley’s Criteria

The Olley Criteria :

1. The front suspension should have a 30% lower ride than the rear suspension.

ba

kk

rear

front .44.11

≅

Rear sprung mass kgkgmrear 8,8001540.52,0 ==→

Front sprung mass kgkgkgm front 2,7398,8001540 =−=→

Front to central of gravities mkgkgm

mm

Latotal

rear 43,11540

8,800.75,2. ===→

Rear to central of gravities mmmb 32,143,175,2 =−=→



mfk n2.4π=

Calculation starts with front sprung mass

comfortHzfmNk

mm

mN

abkk

mNkgHzk

rearn

rear

frontrear

front

→=∴

=

==

==

44,1

45542

32,143,1.44,1.4,29182.44,1.

4,29182)2,739()1(4 22π

Calculation start with rear sprung mass

comfortHzfmNk

mm

mN

bakk

mNkgHzk

frontn

front

rearfront

rear

→=∴

=

==

==

04,1

4,30398

43,132,1.

44,11.5,47421

44,11.

5,47421)8,800()5,1(4 22π

Result

mNk

mNk

rear

front

5,474212,45542

4,303984,29182

−⇒∴

−⇒∴

2. Neither frequency should be greater than 1,3 Hz



For convenience in the analysis the following parameters are defined :

( ) ( )

( ) ( )2

2.

2

.

...

.

kMbkak

Makbk

Mkk

rearfront

frontrear

rearfront

+=

−=

+=

γ

β

α

radius of gyration baDIMI

k y ..==→

Motion of a simple vehicle :

0

0

2 =++

=++••

••

γθβθ

βθα

kZ

zz

with : vertical motion tZz ωsin=→

pitch motion tωθθ sin=→

0sinsinsin2 =++−∴ ttZtZ ωβθωαωω

( )

2

2 0

ωαβ

θ

βθωα

−−=

=+−Z

Z

0sinsinsin 22 =++−∴ ttZ

kt ωγθωβωθω

( )βωγ

θ

22 −−=

kZ



( )

( )( )

( )

( ) ( ) ( ) ( ) ( )2

22

2

222

2,1

2

224

2

222

22

2

4242

0

kk

k

k

k

βγαγαβαγγαγαω

βαγωγαω

βωγωα

βωγ

ωαβ

−−

±+

=⎟⎟⎠

⎞⎜⎜⎝

⎛−−

+±

+=

=⎟⎟⎠

⎞⎜⎜⎝

⎛−+++

=−−

−−=

−−

( ) ( )

( ) ( )2

22

2

2

22

1

42

42

k

k

βγαγαω

βγαγαω

−−

−+

=

−−

++

=

Dynamic Index → DI=1,1

Radius of gyration ( )( )( ) mmmbaDIk 505,132,143,11,1.. ===→

Chose m

Nkm

Nk

rear

front

45542

4,30398

=→

=→

( )

( ) ( ) ( ) ( )

( ) ( ) ( ){ } ( ){ }( )

2

2

22

2

2.

2

2.

2

sec882,41505,11540

43,1.4,3039832,1.45542

...

809,101540

43,1.4,3039832,1.45542.

sec312,491540

455424,30398

−

−

=

+=

+=

=−

=−

=

=+

=+

=

γ

γ

β

α

mkg

mmNmm

N

kMbkak

sm

kg

mmNmm

N

Makbk

kgm

N

Mkk

rearfront

frontrear

rearfront



( ) ( )

( ){ } ( )( )

( ) ( )

( ){ } ( )( )

Hzf

ms

m

k

Hzf

ms

m

k

163,0sec125,6

505,1

809,10

4sec882,41312,49

2sec)882,41312,49(

42

137,0sec327,7

505,1

809,10

4sec882,41312,49

2sec)882,41312,49(

42

2

12

2

2

2222

2

2

22

2

1

11

2

2

2222

1

2

22

1

=→=

−−

−+

=

−−

−+

=

=→=

−−

++

=

−−

++

=

−

−−

−

−−

ω

ω

βγαγαω

ω

ω

βγαγαω

3. The pitch and bounce frequencies should be close together : the bounce

frequency should be less than 1,2 times the pitch frequency.

2,1196,1196,1125,6327,7

2,1

2

1 <→==

<

ωω

pitch

bounce

ff

4. The roll frequency should be approximately equal to the pitch and bounce

frequency.

4.2 Ride and Handling

Ride-handling parameter ζ23ff RH =→

⇒= 1RHf ride - optimized

⇒= 2RHf handling - optimized

⇒−= 75,125,1RHf compromised – design



Chose :

• Sport car 45,0=→ζ ( first assumption is 0,4 )

• ⇒= 1frontRHf ride

• ⇒= 39,1rearRHf compromised

4.2.1 Damping Coefficient Calculation

Damping calculation formula mk

c.2

=→ζ

Front Damper :

ston

skgc

kgmNmkc

f

frontfrontf

27,4275,4266

2,739.4,30398)45,0(2.2

≈=

== ζ

Rear Damper :

rear rear rear

r

Nc 2 k .m 2(0,45) 45542 .800,8kgmkg tonc 5434,138 5,43s s

= ζ =

= ≈

4.2.2 Damping Force Characteristic

Damping force

VmkF ..ζ=

where =V piston velocity

Tension and compression damping force ratio

Tension (m/s) Compression (m/s) Force ratio (T/C)

0.05 -0.05 50/50

0.1 -0.1 60/40

0.3 -0.3 70/30

0.6 -0.6 80/20



Damping force calculation

Speed(m/s) front rear -0.6 -2559.72 -1090.61 -3261 -1304.44 -0.3 -1279.86 -767.81 -1630.5 -978.24 -0.1 -426.62 -341.39 -543.5 -434.88

Tension

-0.05 -213.31 -213.31 -271.75 -271.75 0.05 213.31 213.31 271.75 271.75 0.1 426.62 512.09 543.5 652.32 0.3 1279.86 1791.51 1630.5 2282.56

Compression

0.6 2559.72 4362.45 3261 5217.76



Front Damping Characteristic ( total = left + right )

Front (Total left+right)

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

piston velocity

dam

ping

forc

e

Linear Modif

Rear Damping Characteristic ( total = left + right )

Rear (Total left+right)

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

6000

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

piston velocity

dam

ping

forc

e

Linear Modif



CHAPTER V

RESUME The redesign calculation of Bristol Figther car has accomplished. By satisfying

the consideration of comfort in ride and handling based on the Olley’s Criteria, the

characteristics of the suspension system of Bristol Fighter car are:

1. The value of spring stifnes are:

mNk

mNk

rear

front

45542

4,30398

=→

=→

2. The value of the damper coefficient are:

Front Damper : fronttonc 4,27 s=

Rear Damper : reartonc 5,43 s=

3. The ratio of the pitch and bounce frequency is 1,19 < 1,2



REFERENCES

T. D. Gillespie, T. D. Gillespie, Fundamentals of Vehicle Fundamentals of Vehicle

Dynamics, SAE, 1992

J. J. Reimpell & H. Stoll, The Automotive Chassis: Engineering Principles, SAE, 1996

J.C. Dixon, The Shock Absorber Handbook, SAE, 1999

R.Q.Riley,Automobile Ride, Handling, and Suspension

Design,R.Q.Riley.Enterprise,1999

Documents

Report Example - Car Suspension Design