THESIS FOR THE DEGREE OF LICENTIATE OF ENGINEERING

in

Machine and Vehicle Systems

Truck Steering System and Driver

Interaction

by

KRISTOFFER TAGESSON

Department of Applied Mechanics

CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden, 2014
Truck Steering System and Driver Interaction
Kristoffer Tagesson

c Kristoffer Tagesson, 2014

THESIS FOR LICENTIATE OF ENGINEERING no 2014:16

ISSN 1652-8565

Department of Applied Mechanics

Chalmers University of Technology
SE-412 96 Göteborg
Sweden
Telephone +46 (0)31 772 1000

Chalmers Reproservice
Göteborg, Sweden 2014
 Tilägned Löfåhsen i Sunds Sn
och Inhwånarna afh denna Bygd
Truck Steering System and Driver
Interaction
Kristoffer Tagesson
Department of Applied Mechanics
Chalmers University of Technology

Abstract

This thesis presents a compilation of methods to consider when mapping steering func-
tions and results as vehicle dimensions change. It is concluded that some final tuning
inevitably will be required as major changes are performed. It is however possible to cre-
ate qualified starting points using a set of simple rules as presented. Considered properties
are steering wheel size, wheelbase, steering ratio, and understeer gradient.
An investigation of driver behaviour when a sudden yawing disturbance is acting on
the vehicle is also presented. Two examples, automatic braking on split friction and front
tyre blow-out, are studied in detail. For automatic braking of a heavy truck it is concluded
that current legal requirements and technology for split friction conditions are sufficient
for an alert driver, but may create some problems for a driver being distracted. Most
heavy trucks have positive steering-axis offset at ground, also known as kingpin offset
at ground. This can induce a destabilising steering wheel torque when a front tyre is
damaged. The effect from this is investigated using a qualitative approach. For an active
driver it is found that elimination of the destabilising steering wheel torque has a small,
yet statistically significant, effect on lateral deviation. And furthermore that the lateral
deviation increases as the driver exhibits higher admittance.
A general conclusion from the analysis, on driver behaviour at yawing disturbances, is
that lateral deviation will reduce substantially when driver reaction time is reduced. This
can be achieved by warning the driver prior to the incident. Hence, the warning phase, that
commonly precedes automatic brake activation, is of high importance. Another method
is to use steering support in the initial phase of the incident.

Keywords: active safety, active steering, driver behaviour, heavy trucks, steering system,
torque feedback

i
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List of Included Papers

Paper 1: K. Tagesson, B. Jacobson, and L. Laine, “The influence of steering wheel size
when tuning power assistance,” International Journal of Heavy Vehicle Systems, vol. 21,
no. 4, 2014.
Contribution: The study was designed, run, analysed and authored by Tagesson. Laine
and Jacobson contributed with good ideas and in reviewing.

Paper 2: K. Tagesson, B. Jacobson, and L. Laine, “Driver response to automatic brak-

ing under split friction conditions,” in The 12th International Symposium on Advanced
Vehicle Control, 2014, pp. 666-671.
Contribution: The study was designed, run, analysed and authored by Tagesson. Laine
and Jacobson contributed with good ideas and in reviewing.

Paper 3: K. Tagesson, B. Jacobson, and L. Laine, “Driver response at tyre blow-out in

heavy vehicles & the importance of scrub radius,” in The 2014 IEEE Intelligent Vehicle
Symposium, 2014, pp. 1157-1162.
Contribution: The study was designed, run, analysed and authored by Tagesson. Laine
and Jacobson contributed with good ideas and in reviewing.

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Acknowledgements

The research presented in this thesis has been financially supported by Volvo Group
Trucks Technology and VINNOVA, Sweden’s innovation agency. This support is grate-
fully acknowledged.
I would like to direct my first personal sincere gratitude to my supervisors Adjunct
Prof. Leo Laine and Prof. Bengt Jacobson; always providing motivation, enthusiasm
and insightful comments. Leo’s relentless pursuit towards future visions is unparalleled.
Bengt’s complete eagerness to understand and question everything often triggers the best
ideas. To my managers at Volvo GTT, Stefan Edlund and Inge Johansson. Your incredible
believe in individual creativity is truly honourable. That trust and encouragement make
me grow as a person and in research. Dr. David Cole, thank you for all the shared ideas
and valuable advise you gave during your time as a guest researcher. David, we have some
stuff left; I’m looking forward to it. Thank you Dr. Jochen Pohl for all the time you have
spent to get this project started. My roommate, Peter Nilsson, you gave me inspiration
to actually start doing a Phd. Today I am most grateful for that. And thank you for all
the pleasant chats and cooperation we have had. Thank you Carl-Johan for helping me
out with the trucks. Thank you Gustav and Jan-Inge for linking me into the real world of
steering every now and then. The Vehicle Analysis group at Volvo, big thank you have
all contributed. Adi, Anton, Fredrik, Derong, Gunnar, Artem, Manjurul and Mattias—
surrounded by like-minded gurus what more can I say. The ladies who have helped me
keep track of the oh-so-important administration, Sonja, Marianne and Britta big thanks.
And thank you all others not mentioned for making my days at work enjoyable.
Last but not least, I would like to thank family and friends. You have all contributed
with support, inspiration and joyful moments. Josefin my constant shining light—you
make every day special. Our endless discussions help me navigate through life.

Kristoffer Tagesson
Göteborg, December 2014

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Contents

Page

1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Truck Steering System 7

2.1 Conventional Steering System . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Rack and Pinion Steering System . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Electric Power Steering System . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Angle Overlay System . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Steer-by-Wire System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Mapping Results Between Different Vehicle Types 19

3.1 Vehicle Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Driver Torque Feedback Adaptation . . . . . . . . . . . . . . . . . . . . 20
3.3 Angle Overlay Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 Driver Reaction in Selected Use Cases 25

4.1 Common Ground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 Automatic Braking Activated on Split Friction . . . . . . . . . . . . . . . 26
4.3 Tyre Blow-out & Steering Wheel Forces . . . . . . . . . . . . . . . . . . 28
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5 Concluding Remarks & Future Challenges 33

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2 Future Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Bibliography 39

Paper 1

Paper 2

Paper 3

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Chapter 1
Introduction

This chapter presents the background, motivation and objectives of the thesis. It also gives
the limitations of scope and outline of the thesis.

1.1 Background
During an ordinary walk on a street our brains are able to perceive huge amount of in-
formation every second. Like the feel of a cool breeze against the skin, see a bird fly by
or how you slide on a patch of ice. Each and every impression is composed from end-
less details. All impressions, coming from our senses, are put together and used as we
take continuous decisions. Like lifting a foot, blinking with an eye or stretching out an
arm. All of this is to us evident. It is only by comparison to other systems that our great
capacity becomes apparent.
When seated in a vehicle as a driver, on the same street, continuous decisions will
still have to be taken. Like adding more force on the steering wheel, braking or acceler-
ating. Here, however, our connection to the surroundings has drastically been changed.
The eyesight still works fairly in the same way. Same goes with the sense of balance. But
everything that was perceived using the sense of touch when walking—is now shielded
from the surroundings. Furthermore, the outcome of actions has now another meaning;
turn the steering wheel to change the direction. For us to be able to choose as wise deci-
sions when driving as when walking all of our senses need sufficient information and the
outcome from action needs to be predictable.
The steering wheel is the instrument being used the most by a driver. It is used to
decide on the direction of the vehicle, but also as an extension to the sense of touch. By
holding the steering wheel the driver can feel the motion of the vehicle, the road surface
and forces from the surroundings. We will never be able to sense as much holding a
steering wheel as what we do with our tactile organs on a walk. However steering system
technologies, developed in recent years, at least show that it is possible to add on to
what can be felt in the steering wheel; thereby hopefully supporting the driver. In this
the effectiveness of the design, which lies in being compliant with the human driver, is
the real challenge. In my career I have spent several years in trying to understand what
this means and come to a conclusion; it is only by hard work in trying to understand the
behaviour of a human driver that we can design effective steering. An arrangement where

1
2 CHAPTER 1. INTRODUCTION

all senses are in place for taking important decisions. Continuing on the walk analogy it
is also obvious that the consequences of our actions when driving are often far greater
than when walking. Often we don’t only carry the responsibility of our own lives, but
also others: passengers, pedestrians, cyclists, and other vehicles. Consider driving a 60
ton truck combination. Then obviously all of our senses need sufficient information and
the outcome from action needs to be predictable. Fig. 1.1 shows the enormous forces that
are released in an accident involving a heavy truck.
For sure, road vehicles are and will remain a very important reason for global pros-
perity. Goods and people are transported nationally and internationally for many reasons.
At some locations it is easier and cheaper to grow food. Others have natural resources
available. The sum of only national goods transported on roads, counted in tonnes, within
OECD in 2013 equals moving half of Sweden’s population to the moon1 [1]. As put in
[2], "Transport is important for poverty eradication because it provides access to markets
and supply chains of intermediate outputs." It was even committed by UN General As-
sembly in the Rio de Janeiro 2012 meeting [3] that "We recognize the importance of the
efficient movement of people and goods and access to environmentally sound, safe and
affordable transportation as a means to improve social equity, health, resilience of cities,
urban-rural linkages and productivity of rural areas. In this regard, we take into account
road safety as part of our efforts to achieve sustainable development." Transportation is
evidently an important aspect of the global future development, but equally important is
safety. The consequences of only one fatal accident are huge emotional and economical
losses. According to [4] 1.24 million people were killed and another 20 to 50 million
people got non-fatal injuries on the world’s roads in 2010. Obviously there is a long way
to go.

Figure 1.1: A snapshot from a roll-over test of a heavy truck.

1
Here considering equal payload distance (kilogram-kilometre).
1.2. MOTIVATION 3

1.2 Motivation
Global key risk factors, identified by WHO in [4], for traffic accidents are speed, drink-
driving, motorcycle helmets, seat-belts, and child restraints. WHO recommends an in-
troduction and enforcement of proper legislation as the primal countermeasure for these
factors. Looking at EU only the situation is somewhat different. Even though the number
of vehicles per capita is high the number of fatal accidents per capita is less than half that
of the global level [4, 5]. The simple explanation to this is developed legislation, safer
roads and safer vehicles [4]. Yet, 28,126 fatalities and 1.4 million people injured were
reported in 2012 [6]. In this heavy trucks are involved in about 17% of the fatalities and
7% of all casualties [5]. A general verdict, about these accidents, is given in [5] "Human
error is involved in as many as 90% of all accidents". Looking at heavy trucks only [5]
continues "The two most common human factor related factors that contribute to heavy
truck accidents are failure to look properly and failure to judge another person’s path or
speed. When the vehicle contributes to the accident, the most common cause is limited
visibility due to blind spots."
Based on the details of the findings on accident cause and technology in reach [5] sug-
gests heavy trucks prioritised areas, amongst active safety systems, as: headway support,
lane keeping support, driver awareness support, vehicle stability, vehicle communication,
and visibility support. In common for the first four suggestions is a need of understanding
the interaction between the driver and the steering system. This is the focus of this thesis.
At first headway support might look disconnected from driver steering interaction, but as
will be shown with a recurrent use case it is not.
Two areas, within driver steering interaction, were identified as most valuable to be
able to design effective active safety systems. The first was to find a map between results
received in research on cars and research on heavy truck. The other was to better under-
stand driver behaviour at a sudden lateral disturbance. These two important elements will
be explained more in detail in the following subsections.

1.2.1 Steering Properties Independent on Vehicle Type

There are lane keeping support systems suggested, that alter the steering wheel torque, to
give an indication of where the lane ends, e.g. [7]. There are systems suggested that give
steering guidance to avoid a crash with other vehicles, e.g. [8]. There are systems sug-
gested that provide steering guidance to avoid rolling over the vehicle, e.g. [9]. There are
systems suggested that exaggerate the feel of a slippery road, e.g. [8]. All these systems
are examples of active safety systems where driver steering interaction is on its limits,
i.e. refining the information presented to the driver via the steering wheel to the sense of
touch. Some developed for cars and some developed for heavy trucks. In order to draw
full benefit of the research commissioned on cars when working with heavy trucks, as
said, being able to translate results would be required. For the driver steering task both
vehicle steering response and steering wheel feedback is of value. The obvious differ-
ences in this between a heavy truck and a car are steering wheel size, steering gear ratio
and wheelbase. When searching for previous research in this field very little material is
found. Only a few that can give parts of the answer.
In [10] a fixed base simulator was used to conclude that a driver perceives force rather
4 CHAPTER 1. INTRODUCTION

than torque, here the angular degree of freedom was held fix, known as isometric motion.
When the angular degree of freedom was unlocked and torque set to zero it was further
found that a driver perceives steering wheel, StW, angle rather than hand translation. It
has not been shown how force feedback should scale with StW size in a real vehicle
where isometric motion no longer holds and where the driver subjectively decides on
optimal balance between handling and comfort. Also no such test has been performed
where the subjects are free to choose seating and StW position which could be different
when changing StW. This is the first gap identified.
When working with a more urgent situation a sudden StW torque input would be
tempting to apply, i.e. discontinuous StW torque. For this no in vehicle measurements
have been performed to show differences of driver response when StW size is changed
and where the tension level of the driver is a consequence of the main mission of following
a real road, or similar. This is the second gap identified.
Regarding driver behaviour when changing steering gear ratio or wheelbase there is
already relevant work carried out. For instance Neukum and Ukem [11] tested steering
angle failures on four different cars and gathered subjective ratings on the severity expe-
rienced. They concluded that the subjective rating was independent of vehicle type if the
magnitude of the failure was measured in terms of lateral accelerations or yaw rate. This
is strongly supported in [12] where steering gear ration was altered. It was found that
"yaw rate sensitivity is the actual vehicle steady-state gain characteristic which is noticed
by drivers". By taking account for these and other studies it is possible to suggest how
steering functions should be scaled as steering gear ratio and wheelbase changes.

1.2.2 Driver Behaviour at Sudden Vehicle Disturbance

Driver reaction to sudden lateral disturbance has been studied in e.g. [13]. It is concluded
that the state of mind and body of the driver has large impact on the outcome. Sudden
lateral disturbance in combination with an inattentive driver can be assumed in real traffic
at shifting side wind, side collision, tyre blow-out, or heavy braking on a road section
with significantly different level of friction between left and right vehicle sides. The later
example is commonly known as split friction braking or split-µ braking. Sudden lateral
disturbance in combination with an inattentive driver has been seen to cause severe ac-
cidents in history. For instance tyre failures are involved in many fatal accidents every
year [14, 15]. Again to be able to create effective active safety systems preventing these
accidents detailed understanding of driver reaction is crucial.
For split friction braking a hypothesis is that when the brake action is activated by
an advanced emergency braking system, AEBS, automatically the driver would be less
attentive compared to when the driver activates the brakes. An illustration of the use
case is shown in Fig. 1.2, where an oncoming accident is created after lateral deviation
of a truck combination. The danger experienced and created could therefore increase.
As AEBS, is soon mandatory on heavy trucks in Europe [16] there is a strong need to
gain more knowledge about driver reaction in this particular case. This is the third gap
identified.
The axle installation arrangement used on heavy trucks in general creates a destabilis-
ing steering wheel torque upon front tyre blow-out. This effect is not present on modern
passenger cars. In [17] Pettersson et.al. present the only study found on behaviour among
1.3. OBJECTIVES 5

Figure 1.2: A truck (1) that brakes because of a stationary car (2). A patch of one-sided low
friction (4) causes the truck to yaw and move sideways (5). When adding an oncoming
car (3) into the scene an accident is imminent. The picture is taken from Paper 2.

different drivers at tyre blow-out. The level of StW torque induced was however not var-
ied. This is the fourth gap identified.

1.3 Objectives
The overall objective of this work is to strengthen the knowledge about driver and steering
interaction that can be used in the design of effective active safety functions, developed
to reduce number of traffic accidents. First of all being able to map results and steering
functions from cars to heavy trucks, in this field, constitutes the first main objective of
this thesis. This involves taking account for previous work and carrying out additional
studies to get comprehensive understanding.
The second objective of this thesis is to better understand how drivers react when
brakes are automatically triggered and a yawing disturbance is present, due to e.g. split
friction conditions. This understanding is crucial in order to design robust future headway
support systems.
The third and final objective is to gain knowledge on what consequences a destabilising
StW torque has when a front tyre suddenly explodes.
6 CHAPTER 1. INTRODUCTION

1.4 Limitations
Material, methods and applications that is not handled in this thesis are here listed.

• A destabilising StW torque is also present in a heavy truck during automatic brak-
ing on split friction. This effect is not analysed in here, but might be the subject of
future studies.

• The primal applications of the research presented in this thesis are heavy trucks and
heavy truck combinations. Results will therefore not be discussed for other vehicle
types.

• A one degree of freedom mechanical link in the steering system is assumed if not
otherwise stated. A steer-by-wire installation which is missing this link often pro-
vides more freedom to the design of steering functionality. Today it is however
costly and therefore not treated in here.

• No trailer is included in the experiments performed. Some comments are however

made regarding the inclusion of a trailer, but only from a theoretical point of view.

1.5 Thesis Outline

The thesis is structured as follows. Chapter 2 gathers basic theory about heavy truck
steering systems. Then in Chapter 3 methods on how to translate findings on steering
functions between different vehicle types are described. In chapter 4 driver reaction to
lateral disturbance is treated. Finally, chapter 5 concludes the work and suggest future
priorities. Notations used follow ISO 8855, [18], and units are SI unless otherwise stated.
Chapter 2
Truck Steering System

A steering system provides directional control of the vehicle. This chapter gives an overview
on how the steering system works on a heavy truck and what consequences this has.

2.1 Conventional Steering System

The power required when steering a truck is very high compared to a car. This becomes
obvious when considering the relative difference in front axle load, where a standard car
carry 750 kg and most heavy trucks up to 7,500 kg. The most common front axle steering
arrangement for a heavy truck includes a hydraulic steering gear. A hydraulic steering
gear provides high power in comparison to its volume. Rear drive axles are in general
not steered. However on other rear axles steering is often seen. The steering principles of
these axles are often of simple nature, having the purpose to avoid tyre wear or shorten the
effective wheelbase. Rear axle steering has an effect on vehicle response and manoeuvra-
bility but not directly on steering wheel forces and will therefore not be described further.
The different parts of a conventionally steered front axle on a truck are shown and
explained in Fig. 2.1. A steering wheel angle movement essentially results in a movement
of the steer angle down at the wheels. The left and the right wheel steer angles are tied
together with the track rod. The geometry of how the track rod connects to the steering
knuckles should be chosen to produce a proper level of Ackermann, i.e. more steering on
the inner wheel in corners.
The geometry of the steering knuckle, or more specifically how the kingpin bolt is
oriented, creates the basis for how forces acting on the wheels propagate into the steering
system. In Fig. 2.2 a real installation taken from a Volvo FMX is shown. Of particular
importance are two angles, kingpin inclination and caster. These will be defined in the
following sections. In accordance with [18], X, Y, Z is used to denote the intermediate
axis system, where X is directed horizontally forward on the vehicle, Y pointing hori-
zontally left, and Z pointing upwards. Furthermore the vehicle axis system, XV , YV , ZV ,
is introduced. It is fixed on the vehicle sprung mass so that XV is directed forward on the
vehicle, YV pointing left, and ZV pointing upwards. Note that the vehicle axis system fol-
lows e.g. roll and pitch motion of the sprung mass, whereas the intermediate axis system
does not.

7
8 CHAPTER 2. TRUCK STEERING SYSTEM

1
1
2
2
3 3
4

5
7
8
6
4

Figure 2.1: A conventional steering system from a left hand drive Volvo is shown from front left
hand side, in left subfigure, and from rear, in right subfigure. The steering wheel (1)
is connected via the steering column (2) and the steering shaft (3) to the hydraulic
steering gear (4). The steering gear amplifies the steering wheel torque and produces
a downshift from the incoming shaft angle to the angle of the Pitman arm (5), also
known as drop arm. The Pitman arm is connected via the drag link (6) to the upper
steering arm (7) which is controlling the angle of the steering knuckle around the
kingpin bolt. The left and the right wheel steer angles are made dependent via the
track rod (8).

Figure 2.2: The kingpin bolt, also known as the spindle bolt, is angled to produce proper steering
characteristics. A red line is included to visualise the slant.
2.1. CONVENTIONAL STEERING SYSTEM 9

2.1.1 Kingpin Geometry

The steering axis, also known as kingpin axis, is the axis about which the wheel rotates
relative to the vehicle structure when steered. For a truck with conventional steering this
axis runs through the kingpin bolt. The kingpin inclination angle, σ, is the angle between
the ZV -axis and the steering axis, projected onto the YV ZV -plane, see left part of Fig. 2.3.
The kingpin inclination angle on trucks is normally around 5 degrees, and normally higher
on cars [19]. The lateral component of the distance between road wheel contact centre
and the steering axis, see left part of Fig. 2.3, is known as the steering-axis offset at
ground1 , rk . On heavy trucks the steering-axis offset at ground ranges from 5 cm to 15 cm,
depending on the exact tyre and rim being used. On cars this value is closer to zero or
slightly negative. But again, depending on the exact tyre and rim being used.

σ τ

Z Z
Y X

rk
Figure 2.3: The tilt of the kingpin bolt can be decomposed to kingpin inclination and caster.

2.1.2 Caster Geometry

The caster angle, τ , also known as castor angle is the angle between the ZV -axis and the
steering axis, being projected onto the XV ZV -plane, see right part of Fig. 2.3. For heavy
trucks a typical caster angle is 5 degrees at standstill. Note that during e.g. heavy brak-
ing when the vehicle pitches forward the caster angle will reduce and can even become
negative.

2.1.3 Steering Wheel

Steering wheels can be seen on old cars dating back to around 1900. Before that tiller
steering was the state of art2 . The steering wheel provides two dimensions, steering wheel
1
In ISO 8855 [18] rk is referred to as steering-axis offset at ground or kingpin offset at ground. In [19]
it is referred to as kingpin offset at ground or scrub and in [20] as scrub radius. The term scrub radius
is differently defined in ISO 8855 [18] as the distance from wheel contact centre to the point where the
steering axis intersect ground, i.e. also affected by caster. In this thesis steering-axis offset at ground will
be used to denote rk . However in Paper 2 and Paper 3 rk is referred to as scrub radius.
2
A tiller is a lever which on cars was attached to the steering mechanism. It was directed backwards, as
opposed to what is often seen on boats.
10 CHAPTER 2. TRUCK STEERING SYSTEM

angle, δh , and steering wheel torque, Mh . The relation between these two is here referred
to as steering characteristics. The diameter of the steering wheel is important from two
perspectives. It acts as a lever arm for the driver and it also strongly influences the total
inertia of the steering system. In heavy trucks it is larger as a consequence of legislation.
As stated by [21] the driver should be able to manoeuvre with limited steering forces
also in the case of an assistance failure. This is achieved by designing the steering system
so that the required force to steer the vehicle is limited even without assistance. With
common wheelbase and steering ratio this typically means a steering wheel diameter
of 45-50 cm on modern heavy trucks. Moving away from conventional steering system
arrangements may well change these constraints.

2.1.4 Steering Gear

A hydraulic steering gear is shown in Fig. 2.4. On the incoming axle, from the steering
shaft, a torsion bar is located. This torsion bar causes the opening and closing of valves
for hydraulic high pressure fluid. The steering shaft also turns a ballscrew, known as the
worm. The high pressure fluid is also acting on the worm to amplify the torque applied
by the driver. The other member of the ballscrew causes the outgoing axle to turn the
Pitman arm. The principle is used on most heavy trucks [9]. The design of the valves
within the hydraulics has large influence on the amplification characteristics and therefore
also on the steering characteristics. The amplification characteristics is often visualised
with hydraulic assistance pressure as a function of torsion bar torque, e.g. see [9]. This
curve is known as boost curve. In a heavy truck a common ratio between incoming and
outcoming shaft angle is 16:1 to 27:1. The ratio is often nonlinear with higher ratio closer
to end stops, with the purpose to make the truck manoeuvrable also at loss of hydraulic
assistance [21].

Incoming
shaft

Outcoming
shaft

Figure 2.4: A steering gear provides high power in relation to its volume.

The steering gear together with the linkage geometry produce the overall steering ratio,
is , between the steering wheel angle and the average of the two wheel steer angles, δ.
Where δ is formed by the X direction of the vehicle and the horizontal direction of the
respective wheel. The steering ratio is is defined when no load is applied to the steering
2.1. CONVENTIONAL STEERING SYSTEM 11

system. The ratio is as mentioned before depending on the absolute angle. In a heavy truck
is is in general close to the ratio provided by the steering gear for small steer angles, but
will show a deviation for large steer angles when relay linkages induce nonlinearities.
When loading is added to the steering system, e.g. forces from wheel road interaction,
the actual ratio can deviate substantially from is . This is due to compliance in the steering
system. Here the torsion bar, within the steering gear, dominates [9]. Some trucks might
even produce a steering ratio of double that defined as is when normal load is added [19].
This phenomenon adds understeer as experienced by the driver, since more steering is
required when negotiating a curve at increased speed. Just like the steering ratio down
shifts the steering wheel angle; it up shifts the torque applied on the steering wheel.

2.1.5 Equivalent Wheelbase

Wheelbase, l, is defined for a conventional two-axle vehicle, with a steered front axle and
an unsteered rear axle, as the longitudinal distance between the front and rear axle wheel
contact centre. For vehicles having more than one rear axle the equivalent wheelbase, leq ,
is instead introduced. It describes the wheelbase of a two axle vehicle with similar steady
state turning behaviour as the multi-axle vehicle [22, 18, 23]. When assuming linear tyre
forces the equivalent wheelbase can be calculated as
T CαR
leq = L(1 + 2
(1 + )) (2.1)
L CαF
where L is the wheelbase of the real vehicle calculated as the distance from the front
axle to the point where the moments generated by vertical loads of the rear axles add up
to zero. CαF and CαR are front cornering stiffness and sum of rear cornering stiffnesses
respectively. T is the tandem factor which is calculated as
PN 2
i=1 ∆i
T = (2.2)
N
where N is the number of rear axles and ∆i is the longitudinal distance from axle i to the
rear end of L. From Eq. (2.1) it is seen that a multi-axle vehicle will behave as longer than
its geometrical wheelbase, L. Most linear theory on ground vehicles can be used when
substituting the wheelbase, l, for the equivalent wheelbase, leq , [22].

2.1.6 Steering Response

Steady state steering response of a vehicle is commonly measured in terms of lateral
acceleration gain or yaw velocity gain. Lateral acceleration gain, ∂a Y
∂δH
, is the relation be-
tween change in lateral acceleration and change in steering wheel angle input, where
lateral acceleration is denoted ~aY . In the steady state linear region it holds that

∂aY ~aY ~vX2 1

= = 2
(2.3)
∂δH δH leq + Ku~vX /g is
where Ku is the understeer gradient having the unit rad, ~vX vehicle longitudinal velocity
and g the gravitational constant. Yaw velocity gain ∂ω
∂δH
Z
, is the relation between change in
12 CHAPTER 2. TRUCK STEERING SYSTEM

yaw velocity and change in steering wheel angle input. In the steady state linear region it
holds that

∂ωZ ω
~Z ~vX 1
= = 2
(2.4)
∂δH δH leq + Ku~vX /g is
Fig. 2.5 shows typical steering response for a semi-trailer tractor and a rigid truck as
the longitudinal velocity varies. The relative difference in steering response is obvious
between the tractor and the truck.

Tractor
Truck
0.8 0.35

0.7
0.3
Lateral acceleration gain [g/100o ]

Yaw velocity gain [rad/s/100o ]

0.6
0.25
0.5
0.2
0.4

0.15
0.3

0.1
0.2

0.1 0.05

0 0
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Speed [km/h] Speed [km/h]

Figure 2.5: Typical steering response shown for a semi-trailer tractor unit and a rigid truck.

2.1.7 Ackermann Geometry

In theory left and right wheel steering angles should be chosen so that the rotation axes
always intersect in one point. A point which around all wheels rotate. This would provide
highest degree of manoeuvrability and lowest tyre wear. At low speeds this can be de-
rived purely from vehicle geometry and is known as Ackermann geometry. The relation
between left wheel steer angle, δL , and right wheel steer angle, δR then becomes
1 1 b
= + (2.5)
tan δR tan δL leq
where b is the lateral distance between left and right tyre contact patch, known as track.
An alternative to Ackermann geometry is to have parallel steering, i.e. δL = δR . At high
speeds, where wheels are subjected to high side slip, this can in fact provide improved
manoeuvrability and lowered tyre wear compared to Ackermann.
The steering geometry is in general closer to Ackermann than parallel on heavy trucks.
This is because of the importance of low speed manoeuvrability and that the average
speed is low, c.f. cars. Fig. 2.6 provides an example of the steering relation between left
and right wheels, taken from a heavy truck.
2.1. CONVENTIONAL STEERING SYSTEM 13

50
Measurement
40 Ackermann
Parallel
30
Right wheel steer angle [deg]

20

10

−10

−20

−30

−40
−50 −40 −30 −20 −10 0 10 20 30 40
Left wheel steer angle [deg]

Figure 2.6: The relation between left and right wheel steer angles measured on a specific Volvo
truck. It is obvious that it corresponds a lot closer to Ackermann geometry than the
parallel geometry.

2.1.8 Induced Steering Error

The relay linkages within the steering system will move as the suspension of the vehicle
travels up and down or roll. This will induce a wheel steer angle, disconnected from
steering wheel movement. The relation between the joint, connecting the drag link and
the upper steering arm, and the geometry of the suspension will be the main way of
controlling this effect. The coupling to roll motion, known as roll-steer, in particular is
high on some heavy trucks. This adds understeer (or theoretically oversteer with opposite
sign) as the vehicle rolls in corners. It can also make the vehicle sensitive to vertical
one-sided disturbances.

2.1.9 Steering Forces and Moments

Forces and moments acting on the wheels interact with the steering system. This is well
described in [19]. The most significant terms in this will now be described together with
other torque components acting on the steering system. This gives an overview on all
terms that contribute to the final steering wheel torque, as experienced by the driver. Left
and right wheel steer angles are assumed equal, i.e. small steer angles. Furthermore, caster
and king pin inclination angles are assumed small and symmetric.
To start with the tyre axis system XT , YT , ZT is defined. This system coincides with
the intermediate axis system X, Y, Z, but XT , YT is rotated around the Z-axis so that XT
coincides with the wheel plane. The wheel is subjected to forces and moments in the XT ,
YT and the ZT directions. Forces are denoted as in order F~XT , F~Y T and F~ZT . Moments
are denoted as in order M ~ XT , M
~ Y T and M~ ZT . The later, M
~ ZT , is known as the aligning
14 CHAPTER 2. TRUCK STEERING SYSTEM

moment which has a large impact on the steering system as will be shown.

Resulting Moment from Vertical Force

A vertical force F~ZT is acting on both left and right front wheels, denoted F~ZT L and
F~ZT R . The indices L and R will be used in the remainder as left and right. The resulting
moment acting on the upper steering arm is

MV = −(F~ZT L + F~ZT R ) · rk sin σ sin δ + (F~ZT R − F~ZT L ) · rk sin τ cos δ (2.6)

Here the first term, which includes kingpin inclination, dominates what is experienced
at low speeds in a heavy vehicle. When steering both wheels the vehicle is lifted which
causes a returning moment. The second term, including the caster angle, may cause steer-
ing pull.

Resulting Moment from Lateral Force

The lateral forces F~Y T L and F~Y T R build up with speed when cornering. Road disturbances
can also cause lateral tyre forces. The resulting moment here is

ML = −(F~Y T L + F~Y T R ) · rstat tan τ (2.7)

where rstat denotes wheel radius measured from ground to wheel centre.

Resulting Moment from Longitudinal Force

The tractive forces F~XT L and F~XT R caused by e.g. front wheel drive or more likely brake
activation acts thorough the steering-axis offset at ground and produce a resulting moment
as

MT = (F~XT R − F~XT L ) · rk (2.8)

As rk is positive on heavy trucks it causes a destabilising steering wheel torque during
split friction braking.

Aligning Moment
The resulting lateral force is in general not acting at the centre of the tyre, as assumed
in Eq. (2.7), but further backwards. This distance is known as the pneumatic trail. As
stated by [24], the pneumatic trail will reduce as tyre road friction drops. This makes it
possible to experience a change in friction level even before reaching the actual friction
limit. It should however be stressed that this really requires both a skilled driver and a
steering system free from high friction and damping etc. The resulting moment acting on
the upper steering arm caused by aligning moment, M ~ ZT , is thus
√
MAT = −(F~Y T L · tL + F~Y T R · tR ) cos σ 2 + τ 2 (2.9)
| {z } | {z }
~ ZT L
=−M ~ ZT R
=−M
2.2. RACK AND PINION STEERING SYSTEM 15

where tL and tR denote the pneumatic trail length on left and right wheel receptively,
positive backwards from wheel centre. E.g. the Brush tyre model provides an explanation
of why the pneumatic trail depends on the current friction level and also lateral slip angle
[25]. The pneumatic trail also depends on wheel pressure [24].

Friction Acting on Steering System

The steering system contains several joints, sealing and bearings. All these contribute
with a small amount of friction, i.e. elements slide against each other. Together these
contributions sum up to a total amount of friction within the steering system. Friction can
suppress disturbances, but will also make it impossible for a driver to perceive small force
changes between road and wheel. An example of a model for friction is given in [24]. As
described a simple coulomb friction model is not representative. Therefore [24] suggests
other alternatives, e.g. a spring coupled in series with coulomb friction.
Friction is also present between wheels and road surface at low speeds. This effect of-
ten even produces the highest contribution of moment and can therefore be dimensioning
for the entire system. It is sometimes argued that steering-axis offset at ground would
reduce wheel friction moment. This is shown not to be true in [26] when the wheel is
free rolling. The relation between offset and wheel friction level is very week. When the
wheel is locked the friction moment increases as offset is introduced.

Damping Acting on Steering System

Damping, which is a speed dependent torque is acting within the system in several places.
Damping is stabilising the steering wheel movement. However too much damping will
make the vehicle heavy and slow to steer.

Inertia in Steering System

Steering system inertia mainly comes from the steering wheel itself. This is because of
the ratio acting between the lower and the upper side of the system.

2.2 Rack and Pinion Steering System

Rack and Pinion is a mechanism used on most passenger cars. A pinion is connected to
a linearly moving rack. It contains fewer joints than the steering gear arrangement. This
has the benefit of less compliance and backlash. Heavy truck rack and pinion steering was
introduced by Volvo Trucks in 2012 as they launched the individual front suspension,
shown in Fig. 2.7. The principle of forces, as presented above, acting on the steering
system in Fig. 2.7 still remains however.

2.3 Electric Power Steering System

Electric power steering, EPS, systems consume less energy in general and are easier to
control than hydraulic power steering, HPS, systems [27]. This is the reason why EPS
16 CHAPTER 2. TRUCK STEERING SYSTEM

Figure 2.7: Rack and pinion steering is here used on Volvo’s individually suspended axle. It has
a linear hydraulic piston acting on the rack to provide power steering. The piston can
be seen in the middle of the picture, in silver colour. The axle installation is of type
double-wishbone.

more or less has wiped out the usage of HPS, for high-end passenger cars. For heavy
trucks the story is a bit different. The requirement on power density has made hydraulics
retain its position. The difficulty in controlling hydraulic power steering in an exact and
quick way has however made room for a compromise. A mixture of the two has been
introduced by e.g. Volvo Trucks [28]. A sketch of the system is provided in Fig. 2.8. An
electrical motor is placed on top of a hydraulic steering gear. Both add torque on top of
what the driver does. This is known as torque overlay.
When introducing electronics into the system it is possible to fundamentally change
what is felt in the steering wheel. A pure HPS system can in general only act upon input
from the driver. With electronics introduced it is possible to control the system inde-
pendently of driver input. This is called active steering. With active steering it possible
to have progressive power steering amplification, reduce impact from road disturbances
[28], support the driver with lane-keeping aid functions, and a lot more. It is however not
possible to turn the wheels independently of the steering wheel.

2.4 Angle Overlay System

In [9] an Harmonic Drive gearbox is installed into a heavy vehicle. This makes it possible
to overlay a steer angle on top of the steering wheel angle. Similar systems are used
in some high-end cars. The system, as used in research, in [9] is controlled to induce
artificial understeer and to change the yaw velocity gain. Angle overlay systems provide
an opportunity for changing vehicle response and adding active safety functionality where
2.5. STEER-BY-WIRE SYSTEM 17

Figure 2.8: A combination of EPS and HPS has been introduced on heavy trucks. This picture
shows the system offered by Volvo Trucks. An electric motor (highlighted in blue) is
place on top of a conventional hydraulic steering gear.

the driver can be taken out of the loop to a larger extent than what is possible with a torque
overlay system. Also an angle overlay system can be called active, when it is controlled
independently of driver input.

2.5 Steer-by-Wire System

When removing the mechanical linkage between the steering wheel and the wheels it
is possible to control vehicle response completely independent on driver interaction. It is
also possible to apply any torque onto the steering wheel, completely independent on road
wheel interaction. This is known as steer-by-wire, SbW. Nissan Motor recently introduced
the first commercially available car with SbW. It is characterised with "quick response, a
high disturbance suppression and straight-line capability as well as wide range of steering
ratio settings" [29]. When the mechanical link has been removed very high requirements
on redundancy in electronics are needed. This creates a costly system, which previously
has been the main reason for not having SbW in production cars or trucks.
18 CHAPTER 2. TRUCK STEERING SYSTEM
Chapter 3
Mapping Results Between Different
Vehicle Types

This chapter gives an overview on how steering functions should adapt as vehicle dimen-
sions change.

3.1 Vehicle Differences

In here the fundamental differences between cars and heavy trucks are primarily treated.
Also, when comparing two different trucks great differences are often observed, in length
and number of axles etc. This relation is also considered. Measures from a typical car and
two typical heavy trucks are shown in Tab. 3.1. The table discloses fundamental differ-
ences. The lateral acceleration gains show that a car is a lot more responsive than a truck.
This is mainly due to shorter wheelbase and a more direct steering ratio. The understeer
gradient is also often higher on a truck than on a car. On reason for this is higher compli-
ance in the steering system. The steering wheel torque gradient explains how much torque
that is required to achieve a certain change in lateral acceleration. It should be noted that
the relation between steering wheel torque and lateral acceleration is highly non-linear,
even at low lateral acceleration levels. The gradient is therefore very dependent on the
working point being used. It can be said that the value for trucks is higher than what it is
for cars, but comparing the exact values should be avoided. In summary several properties
differ between a car and a truck. This is also true when comparing different trucks.
Now to the question, how steering functions and results should adapt as physical di-
mensions change? Here considering one dimension at a time. The discussion is divided
depending on whether the function is applying a torque onto the steering system (torque
overlay), or if it is applying an angle (angle overlay). For both of these a distinction is
made between subjective and objective mapping. Subjective conservation is defined as
scaling of a steering function such that the experienced balance between handling and
comfort is preserved after a change in vehicle configuration. And, objective conserva-
tion defined as scaling of a steering function such that the measured vehicle response is
preserved after a change in vehicle configuration. The following sections will describe
scaling of torque feedback where it is considered that one property change at a time.

19
20 CHAPTER 3. MAPPING RESULTS BETWEEN DIFFERENT VEHICLE TYPES

Table 3.1: Specification of a BMW 116i (denoted car), an unloaded Volvo FH 6×2 tractor unit
(truck with a fifth wheel plate), and a fully loaded solo Volvo FH 8×4 rigid timber
truck (truck that can carry payload). All data calculated at 50 km/h. Car data found
in [8] and from supplier specification. The steering response for the two trucks was
previously presented in Fig. 2.5.

Property Car Tractor Truck Unit Description

leq 2.69 3.6 5.9 m Equivalent wheelbase
m 1330 7500 30000 kg Total weight
is 15 20 24 - Overall steering ratio
rStW 0.19 0.225 0.25 m StW radius, measured from centre
to rim edge
Ku 0.015 0.08 0.08 rad Understeer gradient

∂aY
∂δH
0.78 0.3265 0.19 g/100◦ Lateral acceleration gain

∂MH
∂aY
5.86 16 16 Nm/g Steering wheel torque gradient
at ~aY = 0

3.2 Driver Torque Feedback Adaptation

The torque feedback that is present in the steering wheel is composed from all torque
components as described in chapter 2. These are shaped by the power steering system
which e.g. results in a certain level of steering wheel torque gradient, as listed in Tab. 3.1.
There are however a lot more properties that are of importance when describing steering
characteristics. The importance of steering torque has been analysed in several studies
[30, 31, 24]. Different drivers often have different opinions about the optimal level of
feedback [32, 33] when considering subjective rating.

3.2.1 Steering Wheel Size

In [10] it was concluded that a driver perceives force rather than torque. This was based
on a test where the StW angular degree of freedom was locked, known as isometric test.
When the angular degree of freedom was unlocked and torque set to zero it was further
found that a driver perceives StW angle rather than hand translation. In Paper 1 a comple-
mentary study is performed analysing how force feedback should vary with StW size in
a real vehicle where isometric motion no longer holds and where the driver subjectively
decides on optimal balance between handling and comfort. Also analysed is objective
conservation of a steering pulse when StW size changes.

Subjective Tuning of Base Characteristics

A method was developed to scale the complete steering wheel torque in a truck. See
Fig. 3.1 for a visual illustration. A single scaling parameters kg is used to scale all torque
components contributing to the steering characteristics according to
3.2. DRIVER TORQUE FEEDBACK ADAPTATION 21

MH (δH , δ̇H , ~vX ) = kg · MH,0 (δH , δ̇H , ~vX ) (3.1)

where δ̇H denotes steering wheel angular rate, MH,0 baseline steering torque characteris-
tics (solid lines in Fig. 3.1) and kg a scaling parameter.

5
kg =1
kg =0.5
4

2
Driver torque [Nm]

−1

−2

−3

−4

−5
−60 −40 −20 0 20 40 60
StW angle [deg]

Figure 3.1: A method was developed making it possible to scale the complete steering wheel
torque as experienced by the driver, using only one single parameter kg . The char-
acteristics shown is measured at 80 km/h on the truck used in the experiment. From
Paper 1.

A test was run where 17 subjects decided on their preferred value of kg . Each subject
ran with totally three differently sized steering wheels. The steering wheels are denoted as
large, medium and small. This corresponds to a steering wheel radius, rStW , of 0.225 m,
0.195 m and 0.165 m. The test took place on a handling track and subjects were told to
stay between 45 km/h to 90 km/h.
The reported optimal level of kg is shown in Fig. 3.2. The variance in trend between
subjects is large. This is also expected from existing knowledge on the ability of hu-
mans to differentiate steering stiffness. The results indicate that torque feedback should
be scaled when StW size changes. And suggested as a rule of thumb, to use linear scaling
of total torque in order to accomplish maintained driver force level. It was however noted
that further adjustment of damping, friction etc. might be needed to realise conservation
of steering wheel free response return rate.

Objective Evaluation of Pulse Scaling

All 17 subjects also took part in an objective part. They were told to continue driving
around the track with both hands on the StW. Then an operator fired off several StW
torque square pulses. The pulses were 1 s in duration and the size was set to −3 · kg Nm.
22 CHAPTER 3. MAPPING RESULTS BETWEEN DIFFERENT VEHICLE TYPES

Sampled data with count

Constant force
Constant torque
1.1

3
1
17
Normilized selected kg [-]

0.9

0.8 2

0.7
2
3
0.6 2

0.5 2

0.4
0.7 0.85 1
Normalized StW radius [-]

Figure 3.2: kg values are divided with kg from large StW per subject. rStW is divided with rStW
from large StW. Numbers are used to denote multiple occurrence of data-point. Also
included are two lines corresponding to constant force and constant torque respec-
tively. From Paper 1.

Where kg was set in random order to value 1.0, 0.85 or 0.7. These levels roughly corre-
spond to StW radius in relation to the large StW radius. Eq. (3.1) was still applied, i.e.
both the continuous characteristics and the pulse were scaled with kg . This was again
repeated for all three steering wheels.
In total 858 pulses were recorded above 50 km/h, and where no obvious steering mo-
tion was ongoing at the start of the pulse. The relative changes in steering wheel angle
after 0.25 s from these are shown in Fig. 3.3. Not obvious from the figure, but when
looking closer there is in fact a small variation in the response observed for the different
steering wheels. The best match found for preserving driver angular response, and hence
vehicle lateral response, was to scale the torque pulse in inverse relation to StW size, i.e.
preserve StW force. In fact, StW angle change was very similar for all the three steering
wheels when the equal force approach was applied. It is therefore suggested to use the
same rule of thumb as in the subjective section, i.e. use linear scaling of total torque to
accomplish maintained driver force level when StW size is changed.

Common Conclusion
In order to transfer steering functions and map results as the steering wheel size is changed
the common conclusion is that StW force should be conserved. This will ensure both sub-
jective and objective conservation. For the objective part it is important to note that the
force that is applied to the hands of a driver not only originate from the added torque
pulse itself. All other force components, as described in chapter 2, will also have to be
accounted for.
3.2. DRIVER TORQUE FEEDBACK ADAPTATION 23

30 30 30
StW large StW large StW large
Occurrence [-] 20 kg =1 20 kg =0.85 20 kg =0.7

10 10 10

0 0 0
−40 −20 0 20 −40 −20 0 20 −40 −20 0 20
30 30 30
StW medium StW medium StW medium
Occurrence [-]

20 kg =1 20 kg =0.85 20 kg =0.7

10 10 10

0 0 0
−40 −20 0 20 −40 −20 0 20 −40 −20 0 20
30 30 30
StW small StW small StW small
Occurrence [-]

20 kg =1 20 kg =0.85 20 kg =0.7

10 10 10

0 0 0
−40 −20 0 20 −40 −20 0 20 −40 −20 0 20
StW angle change [deg] StW angle change [deg] StW angle change [deg]

Figure 3.3: Histogram of StW angle delta change 0.25 s from the start of the pulse. Mean value
of samples is shown with a vertical line. The y-axis show number of times that the
delta change was observed. From Paper 1.

3.2.2 Steering Ratio, Wheelbase & Understeer Gradient

In [11] it was found that subjective rating was independent of vehicle type if the mag-
nitude of disturbance was measured in terms of lateral accelerations or yaw rate1 . This
is also supported by [12] where it was found that yaw velocity gain is the primary cue
used by drivers when comparing the response between two vehicles. On the other hand
in [9] nine dimensions are identified as important for subjective rating of a vehicle. It is
therefore not practically possible to completely conserve subjective rating of a function
when transferred between vehicle. However just like for StW size some rough rules can
be developed. Starting from the findings in [11, 12] it can be assumed that conservation
of lateral acceleration is consistent with subjective conservation. Objective and subjective
conservation are thereby equal.
Lateral acceleration gain, that is exemplified in Tab. 3.1, can be calculated in the linear
region with Eq. (2.3). It can be seen that a change in overall steering ratio, is , will leave
the lateral acceleration ~aY conserved if δh /is is constant, i.e. leaving road wheel steer
angle unaffected. When changing wheelbase the following relation must hold to conserve
lateral acceleration
∆δH ∆leq
= (3.2)
δH leq + Ku~vX2 /g
where ∆δH is the required change in StW angle to account for a change in equivalent
wheelbase, denoted ∆leq . As seen the adaptation is speed dependent.
1
Yaw rate and lateral acceleration are closely coupled for steady state cornering in the linear region.
Conservation of these two is therefore treated as exchangeable.
24 CHAPTER 3. MAPPING RESULTS BETWEEN DIFFERENT VEHICLE TYPES

A change in the understeer gradient, denoted ∆Ku , can be accounted for in a similar
manner as wheelbase. It results in a required change in StW angle according to

∆δH ∆Ku · ~vX2

= (3.3)
δH gleq + Ku~vX2

From this it can be seen that a change in overall steering ratio, wheelbase or understeer
gradient requires a change in StW angle. This is to be realised using a change in overlaid
steering torque. When applying torque onto the StW the driver responds with hand force.
This process is as seen from Fig. 3.3 coupled to large variance. When no hands are placed
on the StW the required change in StW torque can be calculated from steering character-
istics, see e.g. solid line in Fig. 3.1. When a driver is part of the loop, driver admittance
should also be included, e.g. see [34].

3.2.3 Discussion
When comparing torque overlay results or when mapping a torque overlay function it
is important to consider fundamental physical properties. For StW size this means that
driver force should be conserved. It is here important to recall that all force components
acting in the steering system should be considered.
Other physical properties of high importance are steering gear ratio, wheelbase and un-
dersteer gradient. When these are changed a conservation of lateral acceleration response
should be pursued.

3.3 Angle Overlay Adaptation

An angle overlay function should be scaled for objective conservation. Subjective conser-
vation is not applicable as there is no direct connection to the driver other than via vehicle
response and small StW torque disturbances. Changing the wheelbase or the understeer
gradient would call for adaptation as both wheelbase and understeer gradient influence
vehicle response. As the overlaid angle is commonly applied closer to the wheels Eq. (3.2)
is rewritten for convenience as
∆δ ∆leq
= (3.4)
δ leq + Ku~vX2 /g

where ∆δ denotes the required change in road wheel steer angle to account for a change
in wheelbase. When doing the same thing for a change in understeer gradient it becomes

∆δ ∆Ku · ~vX2
= (3.5)
δ gleq + Ku~vX2
When a steering function is working in a closed loop fashion, i.e. taking in a vehi-
cle state and outputting an overlaid steer angle, it will by nature account for the rela-
tive change in vehicle properties. However control gains should be updated according to
Eq. (3.4) and Eq. (3.5) in order to preserve performance.
Chapter 4
Driver Reaction in Selected Use Cases

In this chapter driver reaction is studied in two different but similar scenarios. To start
with, automatic braking when triggered on a split friction surface. And secondly, front
tyre blow-out.

4.1 Common Ground

As discussed in chapter 1 a driver of a heavy truck is really tested to extremes when
a front tyre explodes. As the tyre is torn to shreds it can produce a lot higher rolling
resistance than a normal tyre. At worst it even stops rolling and instead develops full slip,
similar to a locked up tyre. This will first of all induce a yawing torque on the truck.
It will also exert abnormal forces on the steering system. Furthermore, a truck towing
one or more trailers will experience forces in the connection point because it is only the
towing vehicle that is braked from the disturbance. If an angle has developed, between
the units, this force will act destabilising on the towing vehicle. Combined, these effects
can result in run of road, collision with oncoming vehicles, roll-over or jack-knife, unless
the driver is able to balance the effects by steering or braking. When designing vehicles
it is therefore important to know how a driver reacts at a tyre blow-out.
The other scenario of interest automatic braking on split friction or more general, au-
tomatic braking activated when a yaw disturbance is present. This scenario has a striking
similarity to the blow-out case. It contains all the above elements, a yawing torque, a
destabilising StW torque, and can induce forces in the trailer connection point. The main
differences are the relative levels and that the truck will decelerate more heavily in the
automatic braking case.
In order to better understand driver behaviour in these two cases a test was set up
with a 9 ton solo tractor. All tests were performed on an even test-track with a group of
volunteers. The brake system was first controlled to emulate automatic braking on split
friction. After this blow-out was emulated by locking the front left wheel using the brake.
Paper 2 and Paper 3 contain details on the set-up and outcomes from these two parts
respectively. The following sections give a summary of the experiments and a common
discussion.

25
26 CHAPTER 4. DRIVER REACTION IN SELECTED USE CASES

4.2 Automatic Braking Activated on Split Friction

In this scenario 12 drivers were exposed to sudden automatic braking. They were not
aware of the true purpose of the test in order to preserve the effect from surprise. Drivers
were told that the intention of the test was to record normal positioning in lane and that
they should run back and forth inside a 300 m straight lane. Cruise control was set to
50 km/h. After running back and forth for 5 minutes, without any intervention, an operator
fired of automatic braking. After the first unexpected intervention two repeated runs were
made at the same speed, followed by two more at 70 km/h.
No other vehicle was nearby; therefore cones were put in the adjacent lanes creating a
sense of danger. Fig. 4.1 provides an illustration of the set-up.

50 km/h
3.6m

10m
Automatic braking Soft cone
triggered

Figure 4.1: A sketch of the first exposure of automatic braking with split friction emulated using
the brakes.

4.2.1 Controlling the Brakes

Regulations for AEBS [16] state that the system should be designed to "avoid autonomous
braking in situations where the driver would not recognise an impending forward colli-
sion". This implies that AEBS at least should be capable of decelerating at 3.5 m/s2 during
the emergency braking phase. Here assuming that brake initiation is delayed until TTC
4.0 s, [35, 36], and that the brake system has a delay of 0.2 s from brake request until
full deceleration is reached. Therefore as target deceleration 3.5 m/s2 was used in a brake
controller.
Left to right brake force distribution was determined by running on a real split-friction
area with standard functionality enabled to comply with present legal requirements for
split-friction braking [37]; and where the induced yaw velocity was recorded. The mag-
nitude of yaw velocity was replicated, on a even road, when a fixed ratio of four times as
much brake action was used on left side as on right.
The final brake controller used was a longitudinal acceleration feedback PI-controller
with added feedforward.
4.2. AUTOMATIC BRAKING ACTIVATED ON SPLIT FRICTION 27

4.2.2 Results
All 12 trajectories relating to the very first exposure of automatic braking interventions
are shown in Fig. 4.2. The stopping distance, counting from brake onset, ranges from
30.2 m to 33.3 m. Two drivers instinctively deactivated the intervention by pressing the
accelerator pedal. This corresponds to the two trajectories that continue to travel even af-
ter 35 m. The mean maximum lateral deviation was 0.25±0.07 m, using 95% confidence
level. Two drivers deviated by 0.5 m. All values given in the figure relate to the position
of the drive axle. The mean maximum lateral deviation at the front axle is 4 cm higher
than that of the drive axle, due to the heading of the vehicle. Also included in Fig. 4.2
is an open loop response produced by locking the steering wheel. It deviates by 2.2 m at
standstill.

1.5
[m]

1
E
Y

0.5

0 5 10 15 20 25 30 35
X [m]
E

Figure 4.2: Position of tractor rear axle during unexpected brake intervention, initiated at (0, 0) m.
One black solid curve per driver, thick solid red is average of all drivers, dashed thick
blue is reference run with fixed steering.

Corresponding time series are shown in Fig. 4.3. Looking at the speed curves it can
again be seen that two drivers instinctively deactivated the intervention by pressing the
accelerator pedal. The second subfigure displays change in StW angle, calculated as

∆δH = δH (t) − δH (0) (4.1)

where δH (t) is the StW angle at time t, and t = 0 correspond to brake activation. Some
drivers responded with a smooth and steady movement of the steering wheel, whereas
others oscillated widely. The positive steering-axis offset at ground which acts destabi-
lizing, see Eq. (2.8), can be observed in the StW torque plot. Around -2.5 Nm of the
disturbance reached the driver. As seen in the last subfigure yaw rate is in general shaped
28 CHAPTER 4. DRIVER REACTION IN SELECTED USE CASES

as a one period sine wave. The corresponding frequency, 0.5 Hz, happens to match the
resonance frequency of several truck combination types, see [38].
Speed [km/h]

50

0
0 0.5 1 1.5 2 2.5 3 3.5 4

0
ΔStW angle [deg]

−50

−100

0 0.5 1 1.5 2 2.5 3 3.5 4

2
StW torque [Nm]

0
−2
−4
−6
0 0.5 1 1.5 2 2.5 3 3.5 4
5
Yaw rate [deg/s]

−5
0 0.5 1 1.5 2 2.5 3 3.5 4
Time [s]

Figure 4.3: Response to unexpected brake intervention, starting at time 0 s with a short delay for
brake activation. Line styles same as in Fig. 4.2.

When repeated runs were performed, at 50 km/h, the lateral deviation was nearly
halved on average. The average maximum lateral deviation observed was 0.13±0.03 m,
again using 95% confidence level. The underlying reason for this is identified as shorter
reaction time. In the repeated runs performed at 70 km/h the average maximum lateral
deviation observed was 0.10±0.04 m.

4.3 Tyre Blow-out & Steering Wheel Forces

The positive steering-axis offset at ground which acts destabilizing, see Eq. (2.8), is as
stated of importance as a tyre blow-out occurs. A deflated tyre has a smaller radius than
4.3. TYRE BLOW-OUT & STEERING WHEEL FORCES 29

a normal tyre. The resulting steering-axis offset at ground will hence increase and induce
higher torque onto the steering system, see Eq. (2.8), [39]. In [17] a truck simulator study
was run where it was concluded that the effect of surprise is the main factor to consider,
in order to be able to replicate lateral deviation as observed in real accidents. This is not
targeted in this experiment. Instead the role of steering-axis offset at ground is analysed.
Drivers taking part were not aware of the intention of the test, but had been exposed
to the automatic braking scenario. After this several repetitions of emulated tyre blow-
out was carried out. Cones were again used and put in adjacent lanes to create a sense
of danger and a reason to maintain the intended lane. Data from totally 20 subjects is
included in the analysis that follows.
By using a modified EPS system it was possible to change steering-axis offset at
ground virtually. Two settings were configured 12 cm and 0 cm, where the order used
was varied. Each driver was exposed to three blow-outs per steering-axis offset. The front
left brake was applying 350 kPa. This level was selected just below tyre locking. The
produced tyre force was thereby nearly maximised, but discontinuities relating to ABS
control was eliminated. The relatively high level was selected to produce worst case blow-
out forces, which is still not far above what has been observed during real blow-out, see
e.g. [40]. In the case that the driver pressed the brake pedal a select high pressure routine
was used. If the driver pressed the accelerator pedal the test was aborted.

4.3.1 Results
Fig. 4.4 contains all trajectories produced for front left blow-out runs. Black colour is
used for runs with 12 cm steering-axis offset at ground. Red colour is used for runs with
0 cm offset. Bold lines are used for average. The produced average lateral deviation from
the original direction is 23 cm, when steering-axis offset at ground is 12 cm, compared
to 16 cm on average, when steering-axis offset at ground is 0 cm. There is however large
variance in data, so a direct comparison will not prove a significant difference. Instead
the relative improvement per subject was tested with a paired t-test. This shows that the
average lateral deviation was lowered by 6.4±4.4 cm, using a 95% confidence interval.
This is calculated after 24 m of longitudinal displacement, where the maximum deviation
occurs on average.
Fig. 4.5 contain corresponding time series. Colouring used is the same as in Fig. 4.4.
The speed profiles are as expected similar for all runs apart for some where the driver has
pressed the brake pedal gently. The following subfigure is showing change in StW angle,
as defined in Eq. (4.1). Here, early overshoots indicate that some drivers are affected by
the applied destabilising StW torque. Again a paired t-test was run, showing a significant
difference between 0.3 s and 0.5 s. The StW torque curves show an apparent difference
between the two settings used. From the last subfigure it can be seen that the yaw rate
response roughly show a one period sine wave, c.f. Fig. 4.3. Corresponding frequency,
0.7 Hz, also happens to match the resonance frequency of several truck combination
types.
30 CHAPTER 4. DRIVER REACTION IN SELECTED USE CASES

0.6

0.5

0.4

0.3

0.2
YE [m]

0.1

−0.1

−0.2

−0.3

−0.4
−5 0 5 10 15 20 25 30 35
XE [m]

Figure 4.4: Position of drive axle for all emulated front left blow-out runs. The curves have been
rotated and moved so that blow-out is initiated at position (0,0) m running at zero
heading. Thin red lines correspond to steering-axis offset at ground 0 cm. Thin black
lines correspond to steering-axis offset at ground 12 cm. Bold red line correspond to
average of 0 cm runs. Bold black line correspond to average of 12 cm runs.
4.3. TYRE BLOW-OUT & STEERING WHEEL FORCES 31

Speed [km/h]

40

20

0
0 0.5 1 1.5 2 2.5 3 3.5 4

0
ΔStW angle [deg]

−50

−100

−150
0 0.5 1 1.5 2 2.5 3 3.5 4
2
StW torque [Nm]

0
−2
−4
−6
−8
0 0.5 1 1.5 2 2.5 3 3.5 4

5
Yaw rate [deg/s]

−5

0 0.5 1 1.5 2 2.5 3 3.5 4

Time [s]

Figure 4.5: Time series for all emulated tyre blow-out runs. The blow-out is initiated at time 0 s.
Red lines correspond to steering-axis offset at ground 0 cm. Black lines correspond
to 12 cm.
32 CHAPTER 4. DRIVER REACTION IN SELECTED USE CASES

4.4 Discussion
For the automatic braking case the lateral deviation observed was higher in the first runs,
when drivers were unaware, compared to repeated runs. An identified reason for this
was shorter reaction time. Measured levels suggest that the risk of collision, due to lateral
deviation, is low for an alert driver. For a distracted driver more support might be required.
As was obvious from the repeated runs an aware driver, knowing what will come, is more
effective in reducing lateral deviation. This underlines the fact that the warning phase,
which is already a part of AEBS, is important.
For the blow-out case a small yet significant difference was observed in lateral devia-
tion when steering-axis offset at ground was reduced. The difference would increase for
drivers who do not have a firm grip on the StW. In particular, the improvement for drivers
not holding the StW at all would be several meters. Also the risk of roll-over would be
very high.
In both cases the yaw response frequency matches the resonance frequency of several
truck combinations. It is however not clear if driver response would be identical when
trailers are included.
Chapter 5
Concluding Remarks & Future Challenges

In this chapter the overall conclusions from the thesis are stated. This is followed by ideas
identified for future research.

5.1 Conclusions
The key objective of this work has been to strengthen the knowledge about driver and
steering interaction. This knowledge is intended to be used when designing effective ac-
tive safety functions. The main conclusions from this are here given in a list.

• First of all the theoretical overview on important components, forces, and torques in
the steering system discloses that new technology will enable a paradigm shift. New
technologies like electronic power steering, angle overlay and steer-by-wire open
up for a plethora of functions. The forces acting on the wheels will however remain
and should be taken into account when designing everything from a completely
new steering system to just a new steering function.

• In order to better utilize steering research and development in other areas than the
heavy truck side a lot of attention has been spent on trying to map functions and
results between vehicle platforms. It can be concluded that some tuning will always
be required when functions are e.g. inherited from cars to trucks. It is however
possible to create a set of simple rough rules, describing how to scale functions and
results when important dimensions change. From this the main findings are

– Steering wheel size: Drivers perceive force rather than torque, it is therefore
important to scale steering wheel torque. Here the entire steering characteris-
tics should be considered.
– Steering ratio, wheelbase and understeer gradient: For torque overlay a change
in any of these dimensions will call for scaling of steering wheel torque. The
degree of change is however depending on driver admittance when consider-
ing vehicle response. When the driver is considered out of the loop, it will
be the steering characteristics that will provide the final link for scaling. For
angle overlay the relation is somewhat simpler. Here, it is essentially vehicle

33
34 CHAPTER 5. CONCLUDING REMARKS & FUTURE CHALLENGES

response that should be conserved. This can be derived from basic vehicle
dynamics theory.

• In order to understand driver behaviour when brakes are automatically triggered

and a yawing disturbance is present an experiment was performed emulating split
friction. The conclusions are

– Measured levels suggest that the risk of collision, due to lateral deviation, is
low for an alert driver. For a distracted driver more support might be required.
– A powerful way of reducing lateral deviation is to prepare the driver on what
will come. This will reduce reaction time which has a substantial influence on
the resulting lateral deviation.
– The induced yawing disturbance should be limited based on driver capabili-
ties.
– A reduction in steering-axis offset at ground could potentially reduce the lat-
eral deviation. This has not been investigated.

• Heavy trucks have positive steering-axis offset at ground, also known as kingpin
offset at ground. To better understand what consequences this has in a front tyre
blow-out scenario another experiment was carried out. The conclusions are

– Elimination of steering-axis offset at ground has a small, yet statistically sig-

nificant, effect on the lateral deviation induced at tyre blow-out.
– The main factor for high lateral deviation in a real accident scenario is how-
ever the effect from surprise, as seen in previous research [17], and in the
automatic braking scenario.
– Proper countermeasures for blow-out accidents are identified as, brake based
electronic stability control developed specifically for blow-out, steering guid-
ance, and tyres that cannot blow-out other than slowly.

5.2 Future Steps

Based on the recommendations given, for the two scenarios in focus, it is possible to take
actions. This can potentially save lives in the continuation. In this, the importance of the
truck combination resonance should be analysed further.
Also recommended for future studies is the admittance of a driver to comply with
steering guidance in various scenarios and how this guidance should be designed to be
effective.
In general, when designing vehicle motion support systems, it is important to con-
sider the capacity of the driver to handle possible vehicle disturbances and consequences
thereof. If this is done in real time it would even be possible to design less conservative
systems. E.g. for an automatic braking system the stopping distance, on split friction,
could be reduced when either the driver is in an alert state or when the traffic situation
makes this possible.
5.2. FUTURE STEPS 35

Trucks are driven with trailers. This is often forgotten when considering driver vehicle
interaction. What understanding do truck drivers have about the motion of the trailer?
And is it possible to add on to this understanding e.g. to reduce number of blind spot
accidents? Two questions that exemplify a research field that is still open.
Human drivers can adapt and assess new situations. Computer controlled vehicles can
do boring things millions of times in a reliable and quick way. Let’s make the best out of
this.
36 CHAPTER 5. CONCLUDING REMARKS & FUTURE CHALLENGES
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Paper 1

Title: The influence of steering wheel size when tuning power assistance

Journal: Int. J. of Heavy Vehicle Systems, 2014 Vol.21, No.4, pp.295 - 309

DOI:10.1504/IJHVS.2014.068099

Copyright: c 2014 Int. J. of Heavy Vehicle Systems.

Version: Author’s post-peer review

To cite this article: K. Tagesson, B. Jacobson, and L. Laine, “The influence of steering
wheel size when tuning power assistance,” International Journal of Heavy Vehicle Sys-
tems, vol. 21, no. 4, 2014.

To link to this article: http://dx.doi.org/10.1504/IJHVS.2014.068099

Notation conversions: Td = MH ; Td,0 = MH,0 ; θ = δH ; vx = ~vX

 The Influence of Steering Wheel Size when Tuning Power Assistance 1

The Influence of Steering Wheel Size when Tuning

Power Assistance
Abstract: This paper describes how steering assistance should scale with steering
wheel size. A method has been developed to scale complete torque felt by
the driver, both for continuous and discontinuous feedback. This was used in
an experiment with 17 subjects all driving a truck with three differently sized
steering wheels. The test took place on a handling track at 45 km/h to 90 km/h.
Continuous feedback was evaluated subjectively; discontinuous feedback by
measuring angular response. Results show that torque feedback should decrease as
steering wheel size decreases. A rule of thumb is to keep driver force level constant
to maintain perceived handling and comfort. This also maintained the average
steering wheel angle change response to discontinuous assistance. Furthermore
large variance in angular response was observed. The direction, measured 0.25
s after start of a pulse, was the same as that of the pulse applied in 88% of the
recordings.

Keywords: steering wheel size; tuning; power assistance; steering assistance;

torque feedback; force feedback; trucks; angular response; handling; comfort;
heavy vehicles; steering wheel diameter; steering wheel radius; steering haptics

1 Introduction

Power steering, also known as power assistance, has been used for many years to lower the
required steering effort when turning a vehicle or a vessel (Howe, 1956). In recent years
various more advanced steering systems have emerged. These include new refined methods
for applying assistance torque and changing steering ratio (Heissing and Ersoy, 2010).
Also, they are most often electronically controlled which allows for a greater flexibility in
behaviour. It also opens up for precise tuning of steering support level at every speed and
driving situation.
The steering wheel size, i.e. the diameter, in cars has been kept rather constant
historically. Today it is 35-40 cm in most passenger cars (Wheelskins-Inc, 2009). In heavy
trucks it is larger as a consequence of legislation. As stated by UNECE (2005) the driver
should be able to manoeuvre with limited steering forces also in the case of an assistance
failure. With common wheelbase and steering ratio this typically means a steering wheel,
StW, diameter of 45-50 cm on modern heavy trucks. Until recently truck power steering
systems have exclusively been hydraulic (Volvo-Trucks, 2013; ZF-Lenksysteme, 2012).
When moving away from pure hydraulic power assistance systems and introducing new
redundant electronic steering systems the legislation requirement becomes less relevant.
Hence, the StW size could be chosen more freely also in a heavy truck.
The importance of force feedback for vehicle handling has been analysed in several
studies (Ciarla et al., 2012; Kim and Cole, 2011; Pfeffer, 2006). Anand et al. (2011) carried
out a simulator study where steering effort was tuneable when driving. The subjects reported
their preferred level when satisfied. It was shown that the level varied highly between
2 Tagesson et al.
individuals; this is also confirmed by Barthenheier and Winner (2003). Newberry et al.
(2007) performed a thorough experiment to analyse what aspect of force feedback that a
driver senses - whether it is torque or force. An indoor test apparatus with a strain gauge was
used to measure StW torque. The StW angular degree of freedom was locked (isometric
test). It was concluded that a driver perceives force rather than torque. When the angular
degree of freedom was unlocked and torque set to zero it was further found that a driver
perceives StW angle rather than hand translation. The StW centre position was not adjusted
when changing StW.
It has not been shown how force feedback should vary with StW size in a real vehicle
where isometric motion no longer holds and where the driver subjectively decides on optimal
balance between handling and comfort. Also no such test has been performed where the
subjects are free to choose seating and StW position which could be different when changing
StW. This is the first identified gap analysed in this paper.
Now, continuing on next topic. In recent years new functions have been developed where
more than vehicle forces can be sensed in the StW. Examples are functions for positioning
in lane, crash avoidance and vehicle stabilisation (Rossetter, 2003; Volvo Cars Corporation,
2008; Yang, 2013). Some of these are not continuous, meaning that the torque which is
added to the steering column is ramped up almost instantaneously. The intention is not only
to provide tactile information to the driver. It is also to directly effect the steering wheel
angle before the driver has had time to understand the seriousness of the situation. During
that time the driver is however still in contact with the StW. This highly effects the angular
response of the additional torque.
Cole (2012) developed a driver-vehicle model which was used to analyse a driver’s
ability to do path-following when exposed to a lateral force disturbance. Also driver response
from both angle and torque disturbance inputs was analysed. The model was validated with
a driving simulator experiment where angle overlay was performed. Groups were divided
as tensed or not tensed. Abbink et al. (2011) measured driver frequency response to torque
disturbance in a fixed based simulator. Pick and Cole (2007) used a similar set up to validate
a linear mass-damper-spring model. The angular response was shown to be captured up
to 6 Hz for random torque disturbances. The model contained arm inertia, damping and
stiffness. It was observed that damping and stiffness increased as the driver co-contracted.
Several models have been developed and tests have been performed to study driver
response to discontinuous StW torque feedback. No in vehicle measurements have been
performed to show differences of driver response when StW size is changed and when the
tension level of the driver is a consequence of the main mission of following a real road, or
similar. This is the second identified gap analysed in this paper.
When changing StW size old knowledge about truck steering tuning would have to
be transferred to apply for another StW size. I.e. how steering assistance should be tuned
as a function of StW size. Considered are both continuous properties, e.g. normal driving
characteristics, and discontinuous, e.g. guiding pulse. Hereafter referred to as part 1 and 2
respectively. The work also intends to serve as a mapping when comparing results received
from vehicles with different StW sizes.
This paper describes an experiment conducted on a test track to study:
Part 1 - Tuning of Continuous Characteristics: How continuous steering properties should
depend on StW size to maintain a subjective balance between handling and comfort.
Part 2 - Discontinuous Column Torque: How discontinuous steering properties should
depend on StW size to maintain the same angular driver response.
 The Influence of Steering Wheel Size when Tuning Power Assistance 3
Similar questions could be stated for the properties steering gear ratio and wheelbase. These
are not considered and therefore kept fixed.
In the next section of the paper the developed method for scaling is presented and
the performed experiment is described. In Section 3 received results are presented and
discussed. A conclusion is given in Section 4.

2 Method

In this section basics about steering characteristics are described and also how a scaling
method was applied. The chosen pulse for discontinuous testing is then described. Finally
used vehicle, track and experimental set up are shown.

2.1 Part 1: Continuous Steering Characteristics

Steering assistance systems together with vehicle geometries make up for the basic steering
characteristic, which is of high importance for the experienced stability of the vehicle.
Figure 1 show the basic characteristic properties at vx = 80 km/h, high friction and low
steering wheel angular rate for the truck used in the experiment. A hysteresis, such as
seen in Figure 1, appears due to friction and damping in the steering system. On how to
measure the characteristics, see e.g. (Salaani et al., 2004). The slope and level of hysteresis
of this curve is of high importance to get a comfortable and directionally stable vehicle
(Rothhämel, 2010). The term steering characteristics hereafter refer to the relation between
StW torque and StW angle (with time derivatives). When changing steering wheel diameter

2
Driver torque [Nm]

−1

−2

−3

−4

−5
−60 −40 −20 0 20 40 60
StW angle [deg]

Figure 1 Baseline StW torque characteristics at speed vx = 80 km/h for used truck.

the lever arm for the driver will change. One natural hypothesis would be that the drivers
force level should be kept constant, when steering angular ratio is maintained. In other
4 Tagesson et al.
words the required steering torque should be scaled linearly with steering wheel radius. In
this experiment a truck was equipped with Volvo Dynamic Steering (Volvo-Trucks, 2013).
This allows for great flexibility in shaping the required steering torque. The torque was
changed with a gain factor according to

Td (θ, θ̇, vx ) = kg · Td,0 (θ, θ̇, vx ) (1)

where Td denotes required driver torque, θ steering wheel angle, θ̇ steering wheel angular
rate, vx vehicle longitudinal speed, Td,0 baseline steering torque characteristics (as in Figure
1) and kg a scaling parameter. In Figure 2 characteristics for kg = 0.5 and kg = 1 are shown.
Note that not only the slope but also the hysteresis (damping and friction) is scaled, i.e. the
total torque is scaled with kg at all times.

5
kg =1
kg =0.5
4

2
Driver torque [Nm]

−1

−2

−3

−4

−5
−60 −40 −20 0 20 40 60
StW angle [deg]

Figure 2 Steering wheel characteristic at speed vx = 80 km/h with scaling parameter kg .

If the hypothesis of maintained driver force would hold true the scaling value kg should
have a linear dependence on StW size, for each subject, i.e. each test driver. If on the other
hand the StW torque was to be maintained kg should not change when the StW size varies.
On top of the here described torque characteristics it was possible to superimpose more
torque. This was used in the second part, described in next section.

2.2 Part 2: Discontinuous Steering Characteristics

A discontinuous steering column torque input was produced by a sudden vertical offset to
the characteristics in Figure 2. In the experiment a square pulse was used as discontinuous
torque input. The pulse lasted for one second and was −3 · kg Nm. This gave obvious
impact on the driver but was still considered as safe on the used test-track. The continuous
characteristics were also scaled for part 2 as kg also effect relation (1). Again to scale
complete torque applied on the StW. The rise time of the steering servo motor, from torque
request to actual torque, was below 5 ms.
 The Influence of Steering Wheel Size when Tuning Power Assistance 5
2.3 Experiment

To find out how force feedback should scale with StW size an experiment was set up where
the previously described scaling method was used.

Truck Specification
A rigid Volvo FH16 truck was used. The axle arrangement was a single front axle, two rear
axles whereof one driven. The rear most axle was lifted in all runs. Specifications are shown
in Table 1. Three StWs were used, one Volvo FH 450 mm diameter (large), one Volvo V50
390 mm diameter (medium) and a Sparco R333 330 mm diameter (small). A quick release
was installed to allow fast change of StW.

Table 1 Specification of Volvo FH16 truck used

Property Value Unit Description
L 4.8 m Wheelbase, distance between front
and drive axle
Fz,f 63044 N Front axle vertical load
Fz,d 72275 N Drive axle vertical load
Fz,t 0 N Tag axle vertical load (lifted)
is 23.2 - Steering ratio, road wheel angle to StW
angle
IStW [0.038, 0.019, 0.015] kg m2 StW inertia for large, medium and
small StW including StW and column
above power steering unit
rStW [0.225, 0.195, 0.165] m StW radius for large, medium and small
StW measured from centre to rim edge

The truck was equipped with Volvo Dynamic Steering which is a torque overlay electric
steering servo mounted on-top of a hydraulic steering gear. The servo was controlled with
a dSpace MicroAutoBox to realize scaling as described in section 2.1. In this way the value
kg could be changed from a keyboard even at speed. More in detail, relation (1) was in
fact implemented and verified fully. Including terms for aligning torque, damping, friction,
steering wheel eccentricity and pulse. The only aspect not included in scaling was torque
from StW inertia. The inertia of the StW together with steering column, IStW , was assumed
small enough to be neglected.

Track
A handling track having a lot of bends and one straight section was used. The top speed was
limited to 90 km/h. The track was approximately 3100 m long and 6.5 m wide with two
lanes. Traffic was unidirectional and other vehicles, driving in the same direction, occurred.
The track was dry and some short sections had normal disturbances such as dips, small
crests or were rutted. The maximum lateral acceleration reached by most drivers was around
3 m/s2 . Drivers where advised not to drive slower than 45 km/h. One third of the track had
an alternative route, with more bends. The subject were free to choose their preferred path,
how they positioned and their speed as long as they stayed on road and within speed limits.
6 Tagesson et al.
Subjects
Totally 17 drivers participated; all holding truck driving license. From these 10 were full
time test drivers and 7 development engineers. Two were female. The average driver was
39 years old, got the truck driving license in 1996 and drove 60000 km yearly in a truck.

Set-up
Each person was initially informed about purpose of the activity. This was followed by a
warm up lap to get to know the truck and the track. Then the actual test was run.
Each subject ran with all three StWs. The order of the StWs was randomized. For each
StW subjective tuning of continuous characteristics was first run, then followed by objective
recording of discontinuous response. Here described:
Part 1: Tuning of Continuous Characteristics. The scaling parameter kg was used
to adjust torque level when driving. The initial value of kg was randomized between 0.5
and 1.5, the subjects were told that the initial value was a random number and the actual
value of kg was never shown to subjects. All of this was made to minimize cognitive bias
(Fine, 2008), i.e. anticipation from subjects. The subjects were allowed to drive as many
laps as needed to adjust the value of kg to find their optimal trade-off between comfort and
handling. The subjects were instructed to change the value of kg by requesting either full,
half or a quarter step up or down, where one full step corresponded to 0.1 in delta change of
kg . In this way the subjects were able to actively modify steering force level while driving
and finally report their preferred level.
Part 2: Recording of Discontinuous Column Torque. The subjects were told to
continue driving around the track, put both their hands on the StW and prepare for pulses to
come (c.f. tensed mode in (Cole, 2012)). kg was set in random order to value 1.0, 0.85 or 0.7.
These levels roughly correspond to StW diameter in relation to the large StW diameter. Note
that changing kg effects both continuous characteristics and pulse size and that pulse was
only given in one direction. An operator fired off pulses, unpredictable in time to subject,
and all vehicle signals were recorded.

3 Results and Discussion

Here received results from the two parts are presented.

3.1 Part 1: Continuous Properties

The 17 subjects all decided on optimal scaling values of the driving torque characteristics.
This was done for all the three StWs - resulting in 51 values of kg , see Table 2. In Figure 3
the same data is shown but normalized with respect to the large StW kg value per subject.
The data is normalized since it is assumed that the preferred level is individual. Two lines are
also included to visualise the hypothesis of maintained force and torque. This corresponds
to slope 1 and 0 respectively.
By assuming normal distribution a paired t-test was used to show the likelihood of listed
hypothesis, where three groups were used representing all StW sizes used. The hypothesis
of maintained torque show p < 0.1% and is therefore rejected. The data is a lot more likely
when assuming maintained force. Looking more in detail at the distribution of Figure 3 it
can be seen that the number of data points are too few, as the variance is high, to guarantee
 The Influence of Steering Wheel Size when Tuning Power Assistance 7
Table 2 Final value of kg for all 17 subjects and StWs.
Subject ID Large Medium Small
1 0.9 0.8 0.55
2 1 0.7 0.5
3 0.9 0.85 0.55
4 0.8 0.65 0.5
5 0.9 0.75 0.65
6 0.8 0.65 0.5
7 0.85 0.8 0.55
8 0.8 0.8 0.5
9 0.9 0.55 0.5
10 1 1 0.75
11 1.05 0.8 0.7
12 0.9 0.6 0.7
13 1.05 1 0.7
14 1.15 1.05 0.8
15 0.75 0.75 0.55
16 0.7 0.6 0.55
17 0.9 0.65 0.45

a linear relation. There are other non-linear models that would fit as good or better. The
linear model of maintained force level is therefore only suggested as a rule of thumb for
continuous steering assistance scaling. I.e. can be used as a first good guess.
During the trials some drivers complained about too slow StW free response return when
kg was low, which could suggest a hypothesis of maintained free response return rate. The
steering wheel return acceleration is a consequence of aligning torque minus dissipative
forces, i.e. what is actually scaled with kg . The method for scaling total torque should
therefore only be used as a rough rule of thumb. More precise tuning of e.g. damping would
also be needed, in fact it can be shown that damping should scale as kg2 to maintain free
response return rate. The method used for scaling, where complete torque was varied with
only one parameter, could be extended to make more requirements fulfilled.
Figure 3 show a rather large variance amongst drivers. Some additional tests were
carried out with some of the subjects after completion of the main section. By changing
StW and again initializing kg to a random number the question was if the driver would
replicate his/her previous selection of kg . Most of the subjects were not able to reproduce
their previous value. In fact some drivers were obviously more sensitive than others. Some
needed several laps to feel a difference when kg changed and some felt it instantaneously.
This showed that most of the variance in Figure 3 comes from resolution ability amongst
subjects. The Just Noticeable Difference, JND, describe the minimum difference required
between two stimuli before a human can notice the difference between them. For the arm
joints the JND of sensing force is around 7% and 2 deg for angle (Tan et al., 1994). Assuming
that the subjects compared steering stiffness, in terms of force per StW angle, at 40 deg
the JND for steering stiffness becomes 8.6%, calculated with Taylor expansion of error
propagation. This could explain a large part of the variance in Figure 3. Subjects were not
able to discriminate between settings when kg changed by less than the JND. Whether a
driver perceive force or torque would here be irrelevant, since the relative JND would be the
same. Furthermore whether a driver perceive e.g. lateral acceleration rather than StW angle
8 Tagesson et al.
is left for future work. For this matter it could only add to the JND value, since sensing of
force is here the dominant term. It should also be pointed out that the subjects had to keep
the truck on the road, contributing with more uncertainty.

Sampled data with count

Constant force
Constant torque
1.1

3
1
17
Normilized selected kg [-]

0.9

0.8 2

0.7
2
3
0.6 2

0.5 2

0.4
0.7 0.85 1
Normalized StW radius [-]

Figure 3 Result from test of steering assistance continuous properties. kg values are divided with
kg from large StW per subject. rStW is divided with rStW from large StW. E.g. all
data-points for the large StW will lie in point (1,1). Numbers are used to denote multiple
occurrence of data-point. Also included is two lines, one with slope 1 and one with slope
0, these are constrained to run through point (1,1). The two lines correspond to constant
force and constant torque respectively.

In the actual implementation of (1) it was assumed that torque from StW and column
inertia could be neglected. A recording along the track is shown in Figure 4. It also includes
an estimate of maximum error that is induced when neglecting scaling of inertia. The
estimate is derived from StW angular acceleration times rotational inertia. As can be seen
inertia is a lot smaller than other terms.
Used test procedure was set up to avoid bias in results from subject anticipation. Figure
5 show how initial value of kg effected the final value selected by the subjects. As can be
seen the correlation is very low, which suggests that anticipation from subjects is low. After
the continuous tuning activity all drivers were exposed to several pulses, as described in
Section 2.3, this is the topic of the next section.

3.2 Part 2: Discontinuous Properties

In total 1080 pulses were recorded. Given two conditions, that speed has to be above 50
km/h and that the magnitude of the StW angular rate has to be below 0.2 rad/s prior to pulse,
858 remain. Figure 6 show what effect that the pulses had on the StW angle 0.25 s after start
of pulse. This was the point in time when the highest average deviation was seen. The shape
of the distribution is not a normal distribution as seen. It is not symmetrical around the mean
 The Influence of Steering Wheel Size when Tuning Power Assistance 9

4
Estimated inertia torque difference
Total torque
Friction torque
3

2
Driver torque [Nm]

−1

−2

−3

−4
0 5 10 15 20 25 30 35 40
Time [s]

Figure 4 One measurement of total driver torque and friction along the track together with an
estimate of error in torque arising when neglecting scaling of inertia.

1.3
Large StW data
Medium StW data
1.2 Small StW data

1.1

1
Ending point kg [-]

0.9

0.8

0.7

0.6

0.5

0.4
0.4 0.6 0.8 1 1.2 1.4 1.6
Starting point kg [-]

Figure 5 Final value of kg shown together with the randomized initial value. The correlation is
very low.
10 Tagesson et al.
value and has a long tail on the left side. In total 88% responded in the same direction as the
added torque. Possible reasons for the non-symmetrical shape are varying tension level of
subjects, StW motion prior to the pulse and of course that there is different pulse sizes and
StWs involved. However there are 12% of the pulses that even lead to a response opposite
to the applied pulse. This indicate that the a priori uncertainty of a response is very high.

0.1

0.09

0.08

0.07
Probability [-]

0.06

0.05

0.04

0.03

0.02

0.01

0
−50 −40 −30 −20 −10 0 10 20
StW angle change [deg]

Figure 6 Sampled probability density function of all the 858 pulses. The variable shown is StW
angle delta change 0.25 s from the start of the pulse.

The 858 pulses can be divided into nine classes, three StWs times three different values
of kg . Again mentioned, the pulse size was −3 · kg Nm. For these histograms are shown
in figure 7. Of special interest are the histograms on the diagonal, StW large kg = 1, StW
medium kg = 0.85 and StW small kg = 0.7. These are close to be tuned as suggested in
the rough rule of thumb presented in Section 3.1 - namely scaling of driver torque linearly
with StW size to maintain force. I.e. the continuous characteristics are tuned to maintain
driver force along the diagonal.
Can it also be said that a pulse should be scaled linearly with StW size to preserve driver
angular response? To answer this question two more figures should be considered, Figure
8 and 9. These show how the mean delta change move as time passes. In Figure 8 the pulse
is equal for all the StWs. In Figure 9 the pulse is scaled with StW size. The mean delta
change is almost the same for all StWs, in the latter case, which is not so in the former
case. This supports the hypothesis to scale discontinuous steering torque with StW size. The
uncertainty is however big as seen from pooled standard deviation which is also included
in both figures.
The inertia of the three StWs was not the same. Figure 10 show that the difference in
torque, for the driver, cannot be fully neglected since the pulse itself is of order 3 Nm and
the error up to 0.5 Nm. However inertia conserves energy and the torque absorbed initially
will be released when the motion is decelerated. This would result in a delay of the peak
 The Influence of Steering Wheel Size when Tuning Power Assistance 11

30 30 30
StW large StW large StW large
Occurrence [-]

20 kg =1 20 kg =0.85 20 kg =0.7

10 10 10

0 0 0
−40 −20 0 20 −40 −20 0 20 −40 −20 0 20
30 30 30
StW medium StW medium StW medium
Occurrence [-]

20 kg =1 20 kg =0.85 20 kg =0.7

10 10 10

0 0 0
−40 −20 0 20 −40 −20 0 20 −40 −20 0 20
30 30 30
StW small StW small StW small
Occurrence [-]

20 kg =1 20 kg =0.85 20 kg =0.7

10 10 10

0 0 0
−40 −20 0 20 −40 −20 0 20 −40 −20 0 20
StW angle change [deg] StW angle change [deg] StW angle change [deg]

Figure 7 Histogram of StW angle delta change 0.25 s from the start of the pulse. Mean value of
samples is shown with a vertical line. The y-axis show number of times that the delta
change was observed.
Mean StW angle change [deg]

0
StW large
StW medium
−2 StW small

−4

−6

−8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Pooled standard deviation [deg]

1.5

0.5

0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Delta time [s]

Figure 8 Mean StW angle delta change from start of pulse when kg = 1. Also pooled standard
deviation is seen to grow as time moves.
12 Mean StW angle change [deg]
Tagesson et al.

0
StW large
StW medium
−2 StW small

−4

−6

−8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Pooled standard deviation [deg]

1.5

0.5

0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Delta time [s]

Figure 9 Mean StW angle delta change from start of pulse. For StW large kg = 1, medium
kg = 0.85, small kg = 0.7. Also pooled standard deviation is seen to grow as time moves.

value in Figure 8 when the StW has higher inertia. Only small such tendencies can be seen.
The error induced from inertia is therefore assumed to be of secondary effect.
torque difference [Nm]

1
Estimated inertia

0.5

−0.5
0 5 10 15 20 25 30 35 40
4
StW angle [rad]

−2
0 5 10 15 20 25 30 35 40
Pulse torque [Nm]

−2

−4
0 10 20 30 40
Time [s]

Figure 10 Maximum difference in torque from inertia, StW angle and pulse torque over time from
a recording.
 The Influence of Steering Wheel Size when Tuning Power Assistance 13
4 Conclusions

An experiment has been set up, on a test-track, to show how continuous steering torque
should depend on StW size; this to maintain a subjective balance between handling and
comfort. A method was developed and implemented to scale complete torque felt by the
driver at speed in a truck. 17 subjects tuned torque level for three different StWs, of different
size. Initial scaling was random and not shown to the subjects. Also the order of the StWs was
varied to avoid bias from anticipation. Results indicate that driver torque feedback should
be scaled when StW size changes. A rule of thumb is to use linear scaling of total torque
to accomplish maintained driver force level, which is in accordance with (Newberry et al.,
2007). Further adjustment of damping, friction etc. might be needed to realise conservation
of steering wheel free response return rate. The subjects had some problems to be consistent
in their subjective judgement. The human resolution was identified as the main reason for
this. Further studies on tactile resolution of steering forces are therefore suggested.
Also analysed was how discontinuous steering properties should depend on StW size to
maintain the same angular driver response. I.e. how a torque pulse should scale with StW
size to have the same effect on steering wheel angle, thereby vehicle lateral motion. The
same rule of thumb as for continuous properties was shown to work, namely maintain force
feedback level. The StW angle delta change response was seen to vary a lot. The distribution
was not symmetrical and did thus not follow a normal distribution. In (Cole, 2012; Pick and
Cole, 2007) the cases tensed and relaxed arms differ widely in response. The large variance
here observed could therefore be a consequence of tension level. Other possible factors are
driver arm inertia, strength and if the driver is entering/leaving a turn. By monitoring driver
state it could be possible to reduce the uncertainty in repose (Abbink et al., 2011). This
would be useful when designing steering support functionality and therefore recommended
for future studies.
The study was conducted with fixed wheelbase, fixed understeer properties and fixed
steering gear ratio. These are other possible reasons for having different power assistance
level when varied.

References

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Paper 2

Title: Driver response to automatic braking under split friction conditions

Publisher: JSAE

Copyright: c 2014 Society of Automotive Engineers of Japan, Inc. All rights reserved.

Version: Accepted article

To cite this article: K. Tagesson, B. Jacobson, and L. Laine, “Driver response to automatic brak-
ing under split friction conditions,” in The 12th International Symposium on Advanced Vehicle
Control, 2014, pp. 666-671.

Notation conversions: X = XE ; Y = YE
 AVEC ’14

Driver Response to Automatic Braking under Split Friction

Conditions
Kristoffer Tagesson1,2, Bengt Jacobson1, and Leo Laine1,2,
1
Division of Vehicle Engineering & Autonomous Systems, Chalmers University of Technology
2
Department of Chassis Strategies & Vehicle Analysis, Volvo Group Trucks
Technology

Division of Vehicle Engineering & Autonomous Systems,

Chalmers University of Technology,
Göteborg, SE-412 96, SWEDEN
Phone: (+46) 313234867
E-mail: kristoffer.tagesson@volvo.com; bengt.jacobson@chalmers.se; leo.laine@volvo.com

At normal pedal braking on split-μ a driver can actively steer or adjust brake level to control
lateral drift. The same driver response and thus lateral deviation cannot be assumed when brakes
are automatically triggered by a collision mitigation system, since the driver can be expected as
less attentive. To quantify lateral deviation in this scenario a test was run at 50 km/h with 12
unaware drivers in a heavy truck. Brakes were configured to emulate automatic braking on split-μ.
Results show that the produced maximum lateral deviation from the original direction was 0.25 m
on average. Two drivers deviated by 0.5 m. This can be compared to 2.2 m which was reached
when steering was held fixed.

Topics/Active safety and driver assistance systems, Driver modelling

1. INTRODUCTION depended on if the blow out came as a surprise or not.

Hence it is important to include the effect from surprise
A road section with significantly different level of also when investigating automatic braking under split
friction between left and right vehicle sides is said to friction conditions.
have split friction or split-μ. Common reasons for
split-μ are: oil spillage, uneven ice coating, and
one-sided aquaplaning. When cruising or accelerating
slowly the driver may not even notice the effect, but
when braking hard in an emergency situation the effect
from unbalanced braking forces may cause serious
rotation of the vehicle towards the side of high friction.
For trucks towing one or more trailer this can also lead
to jack-knife [1].
At the event of modest rotation the driver can steer
and balance uneven braking forces. However if the
driver is surprised by the situation and thus unprepared
it is likely that substantial lateral deviation from ego
lane can occur before the driver has responded. This can
result in run of road or collision with oncoming traffic. Fig. 1 An example with a truck (1) that brakes because
Fig. 1 provides an example of this where a truck ends up of a stationary car (2). A patch of one-sided low friction
in the opposite lane. (4) causes the truck to yaw and move sideways (5).
Furthermore a hypothesis is that when braking is When adding an oncoming car (3) into the scene an
activated by an advanced emergency braking system, accident is imminent.
AEBS, automatically the surprise would become even
bigger. And thus also produce bigger lateral deviation
The split friction braking scenario has been a
and higher risk of jack-knifing. One can also note the
well-known hazard for decades and many innovations
similarity to front tyre blow-outs that yearly leads to
have been presented to reduce the effects [4]. Some
some fatal accidents e.g. see [2]. In [3] a truck simulator
have been proven more effective than others. E.g. brake
study was performed where the left front tyre exploded.
pressure limiting approaches are already used on many
It was observed that driver behaviour very much
vehicles, but have the effect of reducing brake
 AVEC ’14

performance. There are also legal requirements for Table 1 Vehicle System Parameters
split-µ braking that limits the allowed lateral deviation, Description Value Unit
under certain conditions [5]. The aim of this paper is to Wheelbase, distance between front and 4.1 m
study if these legal requirements together with drive axle
commonly used functionality are enough, on split-µ, Vehicle width, to outer wheel side 2.25 m
when AEBS is introduced and soon mandatory on heavy
trucks in Europe [6]. Or if there is a need of further Front axle vertical load 58470 N
supporting the driver. Pusher axle vertical load (lifted) 0 N
In order to understand the severity in automatic Drive axle vertical load 29430 N
braking under split friction conditions it is important to
know how a driver reacts. For this reason a test was set Overall steering ratio 23.2 -
up exposing drivers to a rather sudden situation, where Steering wheel radius, measured from 0.225 m
the truck pulls sideways during automatic braking. centre to rim edge
In section 2 the arrangement of the experiment is Wheel effective radius 0.5 m
described, results follow in section 3 and finally section
4 present some conclusions. Notations and properties
used, especially sign conventions, are compliant with
ISO 8855 [8].

2. METHOD

The test was run with a 9 ton solo tractor on a test

track where 12 drivers were exposed to sudden
automatic braking. Research results were obtained
through informed consent. Brakes were controlled to
emulate split-μ conditions on an even test-track. The
drivers were not aware of the true purpose of the test in
order to preserve the effect from surprise. The test was Fig. 2 The test was run at 50 km/h using cruise control.
carefully designed to guarantee safety. Soft cones were used to create a sense of danger.
Only professional drivers, normally driving
durability tests of trucks, took part. The average age was 2.2 Brake Controller
42, the oldest driver was 60 and the youngest 27. Only In [6] requirements implicitly say that an AEBS
one driver had experience from pure brake or handling system shall be capable of performing deceleration by at
tests. Drivers were told that the intension of the test was least 2.2 m/s2 during the emergency braking phase. Also
to record normal positioning in lane and that they stated is that ''the AEBS shall be designed to minimise
should run back and forth inside a straight lane for the generation of collision warning signals and to avoid
300 m. Cruise control was set to 50 km/h. After running autonomous braking in situations where the driver
back and forth for 5 minutes, without any intervention, would not recognise an impending forward collision'',
an operator fired of automatic braking as described. i.e. nuisance should be avoided. In practise this means
After the first unexpected intervention two repeated that the automatic emergency braking phase would have
runs were made at the same speed, followed by two to be triggered closer to the imminent collision. In [9]
more at 70 km/h. normal braking behaviour of drivers in cars is analysed.
At 80 km/h and time to collision, TTC, at 2.7 s it is a
75% chance that a driver would treat the required brake
2.1 Vehicle and Track
action as hard, in order not to collide with a moving
A 6×2 Volvo FH pusher tractor was used in the
target vehicle. In [10] a study on truck driver
experiment having the pusher axle lifted. Since the test
deceleration behaviour was made. At 80 km/h it was
was set up for the first time it was run without any
observed that normal braking does occur as late as TTC
trailers to ensure safety. The same goes with the
3.9 s. This is based on 10000 normal brake interventions
selection of speed. It was low initially to guarantee
from euroFOT data. With the combined findings in [9]
safety. For more details on the vehicle used see Table 1.
and [10] and the requirement regarding nuisance in [6]
The test was run on a test track in Sweden during
an AEBS should at least be capable of decelerating at
two days in December. Temperature was 3-8oC. The
3.5 m/s2 during the emergency braking phase. Here
track was slightly wet, but it did not rain. No other
assuming that brake initiation is delayed until TTC 4.0 s
vehicle was nearby; therefore cones were put in the
and that the brake system has a delay of 0.2 s from
adjacent lanes creating a sense of danger. Fig. 2
brake request until full deceleration is reached (this
provides an illustration of the set-up.
delay was verified on used truck). Therefore as target
deceleration 3.5 m/s2 was used in a brake controller.
The controller consisted of a feedforward and a
 AVEC ’14

feedback part. The feedforward part was constant and responded with a smooth and steady movement of the
the feedback part was a PI controller with integrator steering wheel, whereas others oscillated widely.
saturation and delayed initiation. The positive scrub radius, which acts destabilizing,
The sum of the feedforward part and the PI can be observed in the StW torque plot. Around
controller was fed into a static allocation function. The -2.5 Nm of the disturbance reached the driver.
proportion between left and right brake torque was fix As seen in the last subfigure yaw rate starts building
and set to 4. This value was derived from real split-μ up after 0.3 s and also the response shows a one period
testing, using normal factory brake system settings. In sine wave. Corresponding frequency, 0.5 Hz, happens to
this mode the tractor was compliant with [5] since it had match the resonance frequency of several truck
a brake pressure limiting function setting allowed combination types, see [7]. This highlights the
difference between left and right brake pressure. The importance of extending the study for multi-unit truck
relation between front and rear brake pressure was set combinations.
according to static normal loads. A linear relation was
assumed between brake pressure and brake force. In Fig. Table 2 Brake Control Parameters
3 a block diagram of the controller is shown. All Notation Value Unit
properties included are listed in Table 2.
In case the driver pressed the brake pedal a select Feedback
high pressure routine was used per wheel. If the driver Measured ax - m/s2
pressed the accelerator pedal the test was aborted. longitudinal
acceleration
First order low pass LP - -
filter with time
constant 0.2 s
Target longitudinal ax,ref -3.5 m/s2
acceleration
PI saturation 6000 N
P-gain 4000 N/m/s2
I-gain 20000 N/m/s
Integrator saturation 2000 N
Fig. 3 Block diagram of brake controller PI activation time 1.5 s
PI error linear ramp 0.5 s
3. RESULTS up duration
Feedforward
All 12 trajectories relating to the very first exposure Braking force Kff -18000 N
of automatic braking interventions are shown in Fig. 4.
All lines have been rotated and moved so that (0, 0) m Allocation
correspond to where the operator activated the Total longitudinal Fx - N
automatic braking, i.e. brake onset. The stopping force
distance, counting from brake onset, ranges from 30.2 m Allocation constant Kfl -2.04×10-4 Bar/N
to 33.3 m. Two drivers instinctively deactivated the Allocation constant Kfr -5.10×10 -5
Bar/N
intervention by pressing the accelerator pedal. This -5
Allocation constant Krl -6.79×10 Bar/N
corresponds to the two trajectories that continue to
-5
travel even after 35 m. The mean maximum lateral Allocation constant Krr -1.70×10 Bar/N
deviation was 0.25±0.07 m, using 95% confidence level. Brake pressure Pfl/fr/rl/rr - Bar
Two drivers deviated by 0.5 m. The open loop response (front/rear left/right)
produced by locking the steering wheel, StW, is also
shown. It deviates by 2.2 m at standstill.
Corresponding time series are shown in Fig. 5.
Looking at the speed curves it can again be seen that
two drivers instinctively deactivated the intervention by
pressing the accelerator pedal. The second subfigure
shows StW angle relative change, calculated as:

H(t) = H(t)-H(0) (1)

where H(t) is StW angle at time t. After 0.6 s, on

average, drivers started steering. Some drivers
 AVEC ’14

Fig. 4 Position of tractor rear axle during unexpected

brake intervention, starting at (0, 0) m. One black solid
curve per driver, thick solid red is average of all drivers,
dashed thick blue is reference run with fixed steering.
Lines have been moved and rotated to get zero offset
and heading at beginning.

Continuing with the repeated runs, Fig. 6 and 7 give

all trajectories and time series from the repeated runs.
Four runs have been filtered out since the drivers
pressed the accelerator pedal early on during the
exposure. The average maximum lateral deviation
observed is 0.13±0.03 m, again using 95% confidence
level. There seems to be a reduction in lateral deviation,
as drivers become aware of the true purpose of the test.
To investigate this further a paired t-test was performed
on the StW response. Fig. 8 show average change in
StW angle from both the initial runs and the repeated Fig. 5 Response to unexpected brake intervention,
runs. Also shown is the average difference between starting at time 0 s. Line styles same as in Fig. 4.
these runs per driver. Since each driver conducted only
one initial run and two repeated runs the comparison is
made between the initial run and the average of the
repeated runs. In the four cases where runs are excluded
only one repeated run is used. The difference between
the lines indicate that there is a difference in reaction
time between the runs. This is also clearly confirmed
with the t-test which show a significant difference after
0.5 s, run with 95% confidence level and 11 degrees of
freedom. Looking at the time where the on average
-5 deg is passed the difference is about 0.1 s.

Fig. 6 Position of tractor rear axle during repeated brake

intervention. For line styles see Fig 4.
 AVEC ’14

For the repeated runs done at 70 km/h the lateral

deviation observed was at a similar level as in the
repeated runs done at 50 km/h. The average maximum
lateral deviation observed was 0.10±0.04 m, using 95%
confidence level. The reaction time, before reaching a
StW angle of -5 deg, was again lowered.

4. CONCLUSION

The combination of split-µ and automatic brake

intervention has been tested in a truck with 12 unaware
drivers. Even though drivers were unaware of brake
intervention they were still all aware of being part of a
study and consequently more observant than normal.
The lateral deviation observed was higher in the first
runs, when drivers were unaware, compared to repeated
runs. An identified reason for this was shorter reaction
time. Measured levels suggest that the risk of collision,
due to lateral deviation, is low for an alert driver. For a
distracted driver more support might be required. This
was motivated by the runs where steering was held
locked. As was obvious from the repeated runs a driver
which knows what will come is more effective in
reducing lateral deviation. This underlines the fact that
the warning phase, which is already an important part of
AEBS, should not be underestimated.
Also beneficial would be a low value, or even
negative value, of scrub radius since this limits the
destabilising StW torque which has to be taken care of
by the driver. Using even more sophisticated approaches
for StW torque, like overlay torque guidance, might
even improve the results further. This is however not
obvious.
Angle overlay, steer-by-wire or rear axle steer
systems are other ways of reducing lateral deviation
even further, e.g. see [4]. These also have the potential
Fig. 7 Response to repeated brake intervention, starting of reducing the stopping distance, when combined with
at time 0 s. Line styles same as in Fig. 4. brake controls. Stopping distance is obviously important
when AEBS has activated due to risk of collision.
No major difference in lateral deviation was
observed when increasing speed from 50 km/h to 70
km/h. Drivers did however show shorter reaction time
in this case, most likely since it was the last part of the
test.
Finally said, the yaw rate frequency matched, in
most runs, the resonance frequency of several truck
combinations. It is however not clear whether drivers
respond in the same way when having trailers connected.
Therefore additional tests, including trailers running at a
higher speed, are of importance to completely be able to
investigate the combination of automatic braking on
split friction.

REFERENCES

Fig. 8 Mean value of change in StW angle from the first [1] Zhou, S.W., S.Q. Zhang, &, G.Y. Zhao, “Jackknife
initial runs and from the repeated runs. Also shown is Control on Tractor Semi-Trailer during Emergency
the average difference between the initial run and the Braking”, Adv. Materials Research, Vol. 299-300,
repeated runs. 2011, pp. 1303-1306.
 AVEC ’14

[2] Bareket, Z., D.F. Blower, &, C. MacAdam,

“Blowout resistant tire study for commercial
highway vehicles” The University of Michigan,
Technical report, 2000.
[3] Pettersson, H.E., J. Aurell, & S. Nordmark, “Truck
driver behaviour in critical situations and the impact
of surprise”, DSC Europe, 2006.
[4] Manning, W.J. &, D.A. Crolla, “A review of yaw
rate and sideslip controllers for passenger vehicles”,
Trans. of the Institute of Measurement and Control
29.2, 2007, pp. 117–135.
[5] ECE, “Addendum 12: Regulation No. 13”, Rev. 7,
2011.
[6] EU, “Commission Regulation (EU) No 347/2012”,
2012.
[7] Kharrazi, S., “Steering Based Lateral Performance
Control of Long Heavy Vehicle Combinations”,
Department of Applied Mechanics, Chalmers
University of Technology, 2012.
[8] ISO, “International standard 8855, Road vehicles
and road holding ability – Vocabulary”, 1991.
[9] Kiefer, R.J., LeBlanc, D.J. & Flannagan,
“Developing an inverse time-to-collision crash alert
timing approach based on drivers’ last-second
braking and steering judgments”, Accident; analysis
and prevention, 37.2, pp. 295–303, 2005.
[10] Cheng, Q., “A study of truck driver deceleration
initiation behaviour”, Department of Applied
Mechanics, Chalmers University of Technology,
2012.
Paper 3

Title: Driver response at tyre blow-out in heavy vehicles & the importance of scrub radius

Publisher: IEEE

DOI:10.1109/IVS.2014.6856544

Copyright: c 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must
be obtained for all other uses, in any current or future media, including reprinting/republishing this
material for advertising or promotional purposes, creating new collective works, for resale or re-
distribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Version: Accepted article

To cite this article: K. Tagesson, B. Jacobson, and L. Laine, “Driver response at tyre blow-out in
heavy vehicles & the importance of scrub radius,” in The 2014 IEEE Intelligent Vehicle Sympo-
sium, 2014, pp. 1157-1162.

To link to this article: http://dx.doi.org/10.1109/IVS.2014.6856544

Notation conversions: X = XE ; Y = YE
 Driver Response at Tyre Blow-Out in Heavy Vehicles & The
Importance of Scrub Radius*
Kristoffer Tagesson1 , Bengt Jacobson2 and Leo Laine1

Abstract— Front tyre blow-outs lead to several fatal accidents support drivers by designing vehicles that are insensitive to
involving heavy vehicles. Common for most heavy vehicles tyre blow-outs.
is a positive scrub radius. This can result in a destabilising
steering wheel torque at front tyre blow-out. In this study the There are three different reasons for vehicle instability at
safety improvement achieved when reducing scrub radius is front tyre blow-outs. Firstly, vehicle yaw torque is induced.
quantified. By using a heavy truck equipped with a modified A damaged tyre produces a lot higher rolling resistance than
electric power steering system it was possible to change the a normal tyre. At worst it even stops rolling and instead
scrub radius virtually. Brakes were configured to emulate front
develops full slip, similar to a locked up tyre. Since this force
tyre blow-out which appeared as a sudden disturbance on
one of the front tyres. In total 20 drivers took part in the is offset from vehicle centre a resulting torque around centre
study which was run on a test track at 50 km/h. Results of gravity will be acting. Secondly, common for most heavy
show that the produced average lateral deviation from the vehicles is a positive scrub radius, which is a consequence of
original direction was 23 cm, when scrub radius was 12 cm, wheel and axle geometry. This can result in a destabilising
compared to 16 cm, when scrub radius was 0 cm. The main
cause of the observed difference was a small, yet significant,
steering wheel, StW, torque during front tyre blow-out. A
initial overshoot in steering wheel angle which can be derived deflated tyre has a smaller radius than a normal tyre. This
from the destabilising steering wheel torque. creates even higher scrub radius and consequently also higher
StW torque [3]. Thirdly, a vehicle towing one or more trailers
I. INTRODUCTION will experience forces in the connection point. E.g. if the
towing vehicle is slowed down because of a blown out tyre
Tyre failures are involved in many fatal accidents every a heavy towed trailer will create high forces in the connection
year. In [1] it was found that damaged tyres was the second point. If an angle has developed, between the units, this force
most common vehicle defect reported at fatal accidents will act destabilising on the towing vehicle. Combined, these
between 1995 and 1997 in USA. Blow-outs occurred in effects can result in run of road, collision with oncoming
0.35% of all fatal truck crashes. In particular front tyre blow- vehicles, roll-over or jack-knife, unless the driver is able to
outs seemed more critical than blow-outs on other axles. balance the effects by steering or braking. When designing
In [2] another sample was taken from a French motorway vehicles it is therefore important to know how a driver reacts
network of 2000 km, during the period from 1996 to 2002. at a tyre blow-out. More precisely put, it is important to
It showed that 3.5% of all trucks involved in accidents, with understand driver behaviour as a function of all the three
property damage or injury, were reported with blown out above mentioned instability factors. In this work we focus
tyres. A higher criticality of front axle blow-outs was again on driver behaviour in a heavy vehicle and try to distinguish
confirmed. between vehicle yaw torque and StW torque.
Tyre blow-outs frequency can be reduced using correct Many have studied and modelled the motion of cars and
tyre pressure and thereby avoid overheating. Overloading and trucks at tyre blow-out, e.g. [4] and [5]. Few have studied
excessive wear should also be avoided. Tyre pressure and the variety in behaviour among different drivers at tyre blow-
loading monitoring systems have therefore been suggested out. One exception is [6] where a truck simulator study was
and are already in use on many vehicles [1], [2]. A road run. It was observed that driver behaviour was very much
hazard is another cause of tyre blow-outs. This problem dependent on the effect of surprise. The lateral deviation on
is not removed by previously suggested countermeasures. the first blow-out was a lot higher than on the following trials.
In summary, it can be expected that the total number of The level of StW torque induced was however not varied.
tyre blow-outs on the roads will decline, yet a considerable
To the best of the authors’ knowledge no one has yet
number will remain. It is therefore of high importance to
deeply analysed the influence of StW torque during tyre
*This work was supported by Volvo Trucks and Vinnova
blow-out. In particular not for heavy vehicles where dynam-
1 Kristoffer Tagesson and Leo Laine are with the Division of Ve- ics and steering geometries, e.g. scrub radius, are different
hicle Engineering & Autonomous Systems, Chalmers University of than for cars. This will be the scope of this paper.
Technology. They are also with Department of Chassis Strategies &
Vehicle Analysis, Volvo Group Trucks Technology, 40508 Gothen- The outline of the paper is as follows: In section II
burg, Sweden kristoffer.tagesson@volvo.com respectively the performed test track experiment is described and the
leo.laine@volvo.com corresponding results in section III. Finally some conclusions
2 Bengt Jacobson is with the Division of Vehicle Engineering and Au-
tonomous Systems, Chalmers University of Technology, 41296 Gothenburg, are given in section IV. Sign conventions used for vehicle
Sweden bengt.jacobson@chalmers.se quantities complies with ISO definitions, see [7].
 TABLE I
II. METHOD
S PECIFICATION OF VOLVO FH TRACTOR USED
A test was set up with a 9 ton solo semi-trailer truck,
commonly known as tractor unit, on a test track where Property Value Unit Description
20 drivers were exposed to several repetitions of emulated L 4.1 m Wheelbase, distance between front
and drive axle
front tyre blow-out. Research results were obtained through Fz, f 58470 N Front axle vertical load
informed consent. The test was part of a larger program, e.g. Fz,p 0 N Pusher axle vertical load (lifted)
see [8]. Drivers were not aware of the intention of the test, Fz,d 29430 N Drive axle vertical load
is 23.2 - Steering ratio, road wheel angle to
but had been exposed to three similar interventions prior to StW angle
the blow-out runs, all pulling the vehicle left. rStW 0.225 m StW radius, measured from centre
to rim edge
A. Test Track
The test was run on a closed test track in Sweden during
two days in December. Temperature was 3-8o C. The track to 0 cm of scrub radius in the blow-out case. The system
was slightly wet, but it did not rain. For safety reason a 300 m was made configurable also to function as a conventional
long and 3.6 m wide straight marked lane on a large brake power steering system, however preserving the normal torque
and handling area was used. This provided sufficient safety characteristics, which then is analogous to 12 cm of scrub
margins. To make drivers avoid crossing lane markings soft radius. I.e. the two modes will behave the same during nor-
cones were put in the adjacent lanes. The set-up is illustrated mal driving, but deviate when blow-out occurs. By changing
in Fig. 1. mode in-between runs all drivers were exposed to tyre blow-
outs both with 0 cm and 12 cm of scrub radius.
B. Test Vehicle
The on-board truck sensors were recorded during the
A solo 6×2 pusher tractor was used in the experiment whole test. That includes e.g. yaw rate, lateral acceleration,
having the pusher axle lifted. Brakes were controlled to StW angle, StW torque, wheel speeds, brake pressure, ac-
emulate tyre blow-out. This was performed by applying celerator pedal position and brake pedal position. A high
350 kPa of brake pressure on one of the front tyres. This precision GPS, placed above the drive axle, was also used
level was selected just below tyre locking. The produced and recorded.
tyre force was thereby nearly maximised, but discontinuities
relating to ABS control was eliminated. The relatively high C. Test Drivers
level was selected to produce worst case blow-out forces,
In total 20 professional drivers took part, normally driving
which is still not far above what has been measured, e.g. see
durability tests of trucks. Only one driver had experience
[4]. In the case that the driver pressed the brake pedal a select
from brake or handling tests. The average age was 43.5, the
high pressure routine was used. If the driver pressed the
oldest participant was 63 and the youngest 27. There were
accelerator pedal the test was aborted. Tyre dimensions were
17 male and 3 female.
selected on purpose to get high scrub radius. This resulted
in 12 cm which in the default set up produced around 3 Nm D. Test Procedure
of torque on the StW. For more details on the vehicle used
see Table I. Drivers were told that the intention of the test was to
The vehicle was also equipped with Volvo Dynamic record normal positioning in lane and that they should run
Steering, which is an electric power steering unit. The back and forth inside the straight lane for 300 m. Cruise
system contains the ability to fully suppress steering torque control was set to 50 km/h. An operator fired off emulated
disturbances coming from tyre road interaction, analogous tyre blow-outs on the front left wheel, as described, at
random locations. At the same time cruise control was
deactivated.
Each driver was exposed to three blow-outs per scrub
radius. The order of the exposures was reversed for every
new driver to avoid bias from learning. For some drivers an
additional blow-out on the front right wheel was fired off.

III. RESULTS AND ANALYSIS

All trials have been checked with respect to; initial speed
range 50±2 km/h, correct brake pressure, that the driver did
not press the accelerator pedal, and that the brake pedal was
not pressed hard. After this 103 front left blow-outs remain,
where 51 are run with scrub radius 12 cm and 53 are run with
scrub radius 0 cm. In this series all drivers are represented
Fig. 1. Sketch of track set-up. Soft cones were used to create a sense of in at least one run per scrub radius setting. Additionally, 15
danger in the adjacent lanes. front right blow-outs are also kept.
A. Left Blow-Out Path and Time Series 50

Speed (km/h)
40
Fig. 2 show all trajectories produced for front left blow-
30
out runs. Black colour is used for runs with 12 cm scrub
radius. Red colour is used for runs with 0 cm scrub radius. 20
Bold lines are used for average. The produced average lateral 10
deviation from the original direction is 23 cm, when scrub 0
radius is 12 cm, compared to 16 cm on average, when scrub 0 1 2 3 4
radius is 0 cm. There is however large variance in data, so
a direct comparison will not prove a significant difference. 0
Some drivers deviated left by more than 50 cm.

StW Angle (deg)

Fig. 3 show time series of speed, StW angle, StW torque −50
and yaw rate for all front left blow-out runs. Colouring used
is the same as in Fig. 2. The speed profiles are as expected
similar for all runs apart for some where the driver has −100
pressed the brake pedal gently. The StW angle curves initially
indicate that some drivers, exposed to a destabilising, StW
−150
torque turn left before they turn right. Furthermore during
0 1 2 3 4
the first second the steering profile is rather consistent. After 2
that, very different profiles appear. The StW torque curves
0
show an apparent difference between the two settings used.
StW Torque (Nm)

−2
Continuing on analysing Fig. 3, it can be seen that the
yaw rate response roughly show a one period sine wave. −4
Corresponding frequency, 0.7 Hz, happens to match the
−6
resonance frequency of several truck combination types, see
[9]. This highlights the importance of extending the study −8
for multi-unit truck combinations. 0 1 2 3 4
8

6
0.6
4
Yaw Rate (deg/s)

0.5 2

0
0.4
−2

0.3 −4

−6
0.2
−8
0 1 2 3 4
Y (m)

0.1
Time (s)

0 Fig. 3. Time series for all emulated tyre blow-out runs. The blow-out is
initiated at time 0 s. Red lines correspond to scrub radius 0 cm. Black lines
correspond to scrub radius 12 cm. In the first subfigure drive axle wheel
−0.1 speed is shown. The second subfigure show StW angle which is adjusted to
0 deg at time zero. The third subfigure show StW torque. The last subfigure
show yaw rate.
−0.2

−0.3 In general, drivers that got low lateral deviation responded

early and used high StW angle rate.
−0.4
−5 0 5 10 15 20 25 30 35
X (m) B. Statistical Analysis of Scrub Radius Settings
Trajectories, seen in Fig. 2, StW angle and yaw rate,
Fig. 2. Trajectories of centre of drive axle for all emulated front left seen in Fig. 3, indicate a difference when scrub radius
blow-out runs. The curves have been rotated and moved so that blow- was changed. The variance is however so high that this
out is initiated at position (0,0) m running at zero heading. Thin red lines
correspond to scrub radius 0 cm. Thin black lines correspond to scrub radius
difference is not significant when the two groups are treated
12 cm. Bold red line correspond to average of scrub radius 0 cm runs. Bold as independent, but drivers in the two groups are actually
black line correspond to average of scrub radius 12 cm runs. not independent. The same drivers have been used in both
groups. Therefore we can use a paired difference test to StW angle and yaw rate. The result is shown in Fig. 5 and
analyse the relative change for each driver. By doing so the Fig. 6 respectively. For StW angle we can now prove the
variance used when comparing the groups will be scaled by significance for the groups between 0.3 s and 0.5 s. Drivers
1/n, where n is the number of drivers, in this case 20. The running with scrub radius 12 cm are here pulled by the
two groups will hereafter be denoted as the 12 cm and the disturbing StW torque in the wrong direction before they
0 cm group respectively. react and actively start to balance the blow-out by steering.
In Fig. 4 a paired t-test is performed on the travelled However it should be noted that the significance is not strong.
path data from left tyre blow-outs. First, the average path When using 99% confidence level the difference would not
is calculated for each driver, with the two groups kept apart. prove significant. For yaw rate a difference is also observed.
Then, for each driver, the average path from the 12 cm runs is Here the significance is stronger. A rough estimate show
subtracted from the 0 cm runs. This is shown in black in the that the observed difference in StW angle is large enough to
first subfigure. In other words it is the measured reduction cause the observed difference in yaw rate. And the observed
in lateral deviation for each driver achieved when lowering difference in yaw rate is large enough to cause the difference
the scrub radius. The average of these 20 curves is shown in lateral displacement.
in bold red. After 24 m of longitudinal displacement the
average improvement is 6.4±4.4 cm, using a 95% confidence

Driver StW Angle Difference (deg)

60
interval. 24 m is also where the maximum average displace-
ment is observed in Fig. 2. Fig. 4 also include t-value with 40
19 degrees of freedom. To test if the average reduction is 20
significant a two-tailed t-value with 98% confidence is used.
This gives a t-value threshold of 2.54 which is also marked 0

in the graph (for 99% confidence level the value is 2.86). The −20
98% confidence limit is surpassed after 15 m of longitudinal
−40
displacement. The highest t-value, 3.14, is reached after
21 m. It can therefore be concluded with confidence that −60
drivers are affected by the StW torque they are subjected to. 0 1 2 3 4
3
Also that the lateral deviation is lowered by having a lower
Paired t−value (−)

scrub radius, or as in the case of the tested vehicle a power 2

steering system that eliminates disturbances. 1

0
0.4
−1
Driver Lateral Difference (m)

0.3
−2
0 1 2 3 4
0.2 Time (s)

0.1 Fig. 5. A paired t-test of StW angle. In black the first subfigure show
average StW angle difference per driver between runs with 0 cm scrub radius
and 12 cm scrub radius. The red bold curve is the average of all drivers.
0 The second subfigure show the corresponding t-value, in solid black. Also
included is a dashed blue line at 2.54 which is equal to t19,0.99 , i.e. the
−0.1 two-sided 98% cumulative probability value for 19 degrees of freedom.

−5 0 5 10 15 20 25 30 35

C. Open Loop Response

Paired t−value (−)

2
Fig. 7 show all trajectories, just like Fig. 4, but here a
0 dashed green line is also included to show the open loop
vehicle response. I.e. a run where StW angle was locked
−2 at 0 deg. For this run the lateral deviation quickly becomes
−5 0 5 10 15 20 25 30 35
X (m) more than a lane. The importance of having an alert driver
is obvious.
Fig. 4. A paired t-test of trajectories. In black the first subfigure show D. Subjective Comparison of Scrub Radius
average lateral difference per driver between runs with 0 cm scrub radius
and 12 cm scrub radius. The red bold curve is the average of all drivers. The virtual change made of scrub radius between the first
The second subfigure show the corresponding t-value, in solid black. Also
included is a dashed blue line at 2.54 which is equal to t19,0.99 , i.e. the
and the last trials was kept secret to the drivers. Directly after
two-sided 98% cumulative probability value for 19 degrees of freedom. the last run all drivers were asked if they had experienced any
difference. Some reported that they had perceived the distur-
To get a better understanding of the cause of the improve- bance at blow-out as higher in some of the runs compared to
ment identified we perform the same paired test also for others. Objectively, the level of the disturbance was the same
 for all runs. No one reported that they had felt a difference
connected to steering. As a follow-up question, all drivers
Driver Yaw Rate Difference (deg/s)

4
were also asked if they had experienced any difference in
2 the steering system. No one had. In Fig. 3 the difference
in terms of steering wheel torque is apparent between the
0 two settings. About 3 Nm of disturbance reaches the driver
−2
when scrub radius is 12 cm. As a separate experiment 3 Nm
was applied to the StW during normal driving for a few
−4 drivers. All noticed that a disturbance had been applied. The
difference between the normal and the critical situation is
−6
obviously an example of how the mental ability, to perform
6
0 1 2 3 4 concurrent tasks, is dependent on the intensity of the main
task.
Paired t−value (−)

4
E. Right Blow-Out
2
Some drivers were also exposed to a blow-out on the
0 right front wheel directly after the main series of blow-
−2
outs on the front left wheel. Fig. 8 show trajectories for
0 1 2 3 4 these runs. The average lateral deviation produced increased
Time (s) compared to left-blow out runs. Drivers had become used to a
disturbance on the left front wheel. In line with [6] this show
Fig. 6. A paired t-test of yaw rate. In black the first subfigure show that repeated exposures will reduce the lateral deviation, as
average StW angle difference per driver between runs with 0 cm scrub radius
and 12 cm scrub radius. The red bold curve is the average of all drivers. the driver focus harder and learn the manoeuvre.
The second subfigure show the corresponding t-value, in solid black. Also
included is a dashed blue line at 2.54 which is equal to t19,0.99 , i.e. the
two-sided 98% cumulative probability value for 19 degrees of freedom.

0.2

4
0

3.5
−0.2

3
Y (m)

−0.4
2.5

−0.6
2
Y (m)

1.5 −0.8

1 −1

0 5 10 15 20 25 30 35
0.5 X (m)

0
Fig. 8. Trajectories for all emulated front right blow-out runs. The curves
have been rotated and moved so that blow-out is initiated at position (0,0) m
−5 0 5 10 15 20 25 30 35 running at zero heading. Thin red lines correspond to scrub radius 0 cm.
X (m) Thin black lines correspond to scrub radius 12 cm.

Fig. 7. Trajectories for all emulated left right blow-out runs in comparison
to an open loop response. The curves have been rotated and moved so that IV. CONCLUSION
blow-out is initiated at position (0,0) m running at zero heading. Thin red
lines correspond to scrub radius 0 cm. Thin black lines correspond to scrub
A test was set up with a 9 ton solo tractor on a test
radius 12 cm. Bold dashed green line correspond to the open loop response, track where 20 drivers were exposed to repeated exposures
i.e. StW angle locked at 0 deg. of emulated worst case front tyre blow-outs. By using a
configurable power steering system it was possible to alter
between two scrub radius settings, one corresponding to [7] ISO, “International standard 8855, Road vehicles and road holding
12 cm and one to 0 cm. It was observed that the lateral ability - Vocavulary,” 1991.
[8] K. Tagesson, B. Jacobson, and L. Laine, “Driver response to automatic
deviation produced at a blow-out was lowered by 6.4±4.4 cm braking under split friction conditions,” in Submitted to AVEC, Tokyo,
when scrub radius was changed from 12 cm to 0 cm. The 2014.
difference would increase for drivers holding the StW loose. [9] S. Kharrazi, “Steering based lateral performance control of long heavy
vehicle combinations,” Ph.D. dissertation, Chalmers University of Tech-
In particularly, the improvement for drivers not holding the nology, 2012.
StW at all would be several meters. Low scrub radius or
a power steering system, that removes disturbances, could
therefore ultimately slightly reduce the number of fatalities
caused by tyre blow-outs.
Results also reveal that the response received from differ-
ent drivers vary widely at a blow-out, irrespective of scrub
radius setting. This is for instance reflected in reaction time
and steering rate. These two measures have been identified as
very important as to be able to maintain low lateral deviation.
The test was set up with drivers that knew they would be
exposed to some sort of challenge. As seen in [6] it is
therefore most likely that e.g. reaction time would be higher
under normal circumstances, as also partly was confirmed
with results from right front tyre blow-outs. On average there
is a statistically significant improvement of lowering scrub
radius, but for an inattentive and less skilled driver yet more
support would be needed to secure all scenarios.
To further reduce the number of accidents involving de-
fective tyres there are several additional solutions that can
be developed. First observation, reaction time is obviously
critical. Designing tyres that always deflate slowly at the
event of failure would therefore be beneficial. Developing
stability support using brakes or additional steering, to re-
duce the initial heading error, would be another method.
Using stabilising steering torque could be a third way. Next
observation, when considering a vehicle combination with
more than one unit the dynamics of the full vehicle must
be considered. Here knowledge about driver behaviour is
missing. When this information is available all previously
suggested methods may need adjustments. And final obser-
vation, all drivers being part of this study had improved their
deviation when exposed to a blow-out by the end of the
session. Practical training should not be underestimated.
R EFERENCES
[1] Z. Bareket, D. F. Blower, and C. MacAdam, “Blowout resistant tire
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