Final Report

Faculty of Technology, Design and Environment
MASTER OF SCIENCE DISSERTATION
Title: Analysis of the steady aerodynamic forces generated by
road cars in crosswind conditions using a simple bicycle model
and CFD
Surname: Bracho
First Name: Jose Javier
Supervisor: Dr. Daniel Bell
Student No.: 12071817 Date Submitted: 21/09/2013
Module No.: P04796
Subject Title: MSc Automotive Engineering Project

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not been submitted for any degree at this or any other academic or professional institution.
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Analysis of the steady aerodynamic
forces generated by road cars in
crosswind conditions using a simple
bicycle model and CFD
Oxford Brookes University
Jose Javier Bracho
Student No.: 12071817
MSc Automotive Engineering
Department of Mechanical Engineering and
Mathematical Sciences
August 2013
Project Supervisor: Dr. Daniel Bell

ABSTRACT
Ground road vehicles exposed to crosswind situations present a complicated
challenge not only to drivers but also automotive designers in constant concern of
handling and safety. The modelling of these conditions is rather difficult due to the
complexity of the scenario where aerodynamics, vehicle dynamics and driver’s
reactions interact with each other. The aim of this project is to integrate the analysis
of static aerodynamic forces into a comprehensive bicycle model, capable of
measuring the impact of general design parameters into the crosswind sensitivity of a
vehicle. Implementing a Reynolds-Averaged Navier-Stokes equations (RANS)
simulation, aerodynamic forces and moments are calculated to then be coupled with
a two-degree of freedom bicycle model measuring parameters such as: yaw rate and
lateral displacement. A parameter study regarding general vehicle dynamics features
is carried out to determine which is the most influential to yaw rate. Flow structure
asymmetry created a significant discrepancy in forces experienced along the
vehicles, resulting in yawing moments turning the cars away from wind direction.
Three basic vehicle geometries were considered, indicating an inversely proportional
relationship between rear side area distribution and yaw moment experienced.
Stability in these scenarios was found to be linked not only to aerodynamic features
but mainly to vehicle dynamic properties such as tyre size and weight distribution. It
was showed that the motion of the centre of pressure with respect to the locations of
the centre of gravity and the neutral steering point is the main interest to design
vehicles less sensitive to crosswind situations.
Key words: crosswind sensitivity, vehicle dynamics, RANS simulation.

ACKNOWLEDGEMENTS
I am thankful to Oxford Brookes University for the constant support and kind
assistance which turned each difficulty into a great opportunity to learn and develop
myself as a better professional.
I would like to thank my supervisor, Dr. Daniel Bell, for all his guidance, time devoted
and his endless will to support and help not only me, but all the group of students
who were taking part in aerodynamic related projects.
Thanks to Dr. James Balkwill for his invaluable lessons and for sharing that immense
passion that showed me how to be excellent at your profession.
To all the rest of the teacher staff in the Department of Mechanical Engineering and
Mathematical Sciences, who were always willing to take a moment to discuss and
give appropriate advice to any source of problems students presented them.
To my colleagues, who taught me and help me every time I needed them, sharing all
their knowledge and experience as well as their friendship making this a great
experience. I’ll never forget.
To my family, for giving me the opportunity to grow and fulfil my dream of becoming
an Automotive Engineer and an unlimited source of wisdom and guidance. This is for
you.
To my girlfriend, for making the distance become a strong incentive to give my best
as a person and her endless love and caring that kept me going especially in the
most difficult times.
i

TABLE OF CONTENTS
Acknowledgements i
Table of Contents ii
List of Figures/Diagrams iii
List of Tables iv
List of Symbols and Abbreviations v
1 Introduction 1
2 Literature Review 5
2.1 Ground Vehicle Aerodynamics 5
2.2 Previous studies on crosswind 9
2.3 Analytical modelling of crosswind and numerical investigations 14
2.4 Crosswind sensitivity 17
3 Methodology 19
3.1 Vehicle models 19
3.2 RANS simulations of steady state crosswind 21
3.3 Vehicle dynamics simulations of a simple bicycle model 24
3.4 Parameter study 26
4 Results and discussion 28
4.1 Computational fluid dynamics results 28
4.2 Vehicle dynamics results 33
4.3 Parameter study results 37
5 Conclusions and further work 40
References 42
Appendices 46
ii

LIST OF FIGURES/DIAGRAMS
Chapter 2
Figure 2.1: Boundary Layer on a flat plane 7
Figure 2.2: Vehicle aerodynamic forces and moments representation while
driving into a crosswind 8
Figure 2.3: Reference frame used for the CFD models 9
Figure 2.4: Resultant flow velocity in a crosswind situation 9
Figure 2.5: Division between quasi-steady and transient approaches for
crosswind 11
Figure 2.6: Asymmetrical pressure distribution at yawed condition causing a
leeward steering effect 11
Figure 2.7: Steady increase of yaw moment within relevant range of yaw angle 12
Figure 2.8: Isosurface of total pressure at 1.6 degree yaw angle 16
Figure 2.9: Pressure coefficient at the windward lateral surface of the trailer 17
Chapter 3
Figure 3.1: Dimensions of MIRA reference car model 20
Figure 3.2: Computational domain dimensions and boundary conditions 22
Figure 3.3: Visual detail of trimmer mesh, volumetric control and prism layer
selected 23
Figure 3.4: Conventional bicycle model 24
Chapter 4
Figure 4.1: Isometric pressure plots for FB, NB and SB models 29
Figure 4.2: Pressure distribution around the FB, NB and SB models 30
Figure 4.3: Velocity magnitude around the FB, NB and SB models 31
Figure 4.4: Yaw rate for the FB, NB and SB models 34
Figure 4.5: Lateral displacement for the FB, NB and SB models 34
Figure 4.6: Driver controlled and stable reaction compared to natural unstable
mechanical responses of a vehicle to a sudden side gust 36
Figure 4.7: Lateral displacement improvement after applying the balancing of
parameters 38
Appendices
Figure A.1: Diagram for the linking of CFD and vehicle dynamics models 47
iii

LIST OF TABLES
Chapter 3
Table 3.1: Dimensional details of the MIRA reference car models 20
Table 3.2: Optimum mesh values for vehicle aerodynamics 22
Table 3.3: Vehicle models selected for mass related parameters 26
Chapter 4
Table 4.1: Aerodynamic forces and moments net values 32
Table 4.2: Test matrix and parameter study for the FB model 37
Appendices
Table A.1: CFD baseline models validation 49
iv

LIST OF SYMBOLS AND ABBREVIATIONS
Upper-case Roman
A frontal area
CD drag coefficient
CL lift coefficient
CP pressure coefficient
CSide side force coefficient
CYaw yaw moment coefficient
L vehicle length
Lf Lift force
Re Reynolds number
ReL Reynolds number based on the vehicle length
Re√A Reynolds number based on the square root of the frontal area
U travelling speed of the vehicle
Ur incident velocity
U∞ free stream velocity
Ui,j velocity gradient
W (cross)wind speed
WT Total weight of the vehicle
Wcar Specific weight of the vehicle
Wdriver Specific weight of the driver
Lower-case Roman
f frequency
h vehicle height
l vehicle width
p pressure
v

t time
y+
non dimensional wall unit
Lower-case Greek
𝑣 kinematic viscosity
k turbulent kinetic energy
Superscripts
° angle degree
Symbols
∇ gradient
𝜕 partial derivative
𝑈��⃗ velocity vector
Abbreviations
CFD Computational Fluid Dynamics
CoG Centre of Gravity
CoP Centre of Pressure
CS Cornering Stiffness
DES Detached Eddy Simulations
DNS Direct Numerical Simulation
FB Fastback
LES Large Eddy Simulations
NB Notchback
NS Navier-Stokes equations
NSP Neutral Steer Point
RANS Reynolds-Averaged Navier-Stokes equations
SB Square-back
vi

Chapter 1
INTRODUCTION
This chapter is aimed to present the adequate outline of the investigation including all
the pertinent information leading to the interest and relevance of executing this
project. Preliminary information and general knowledge on the challenges of
crosswind analysis is given, along with an outline of the objectives to accomplish
during the study. An overview of the project is given at the end of this chapter.
Background
Stability and safety are always focused within the designing process of automobiles,
considering every possible situation the vehicles might be exposed to, and controlling
their performance. Aerodynamically speaking, probably the most popular and known
approach is perceived in drag reduction to enhance fuel economy, decreasing the
resistance a vehicle geometry offers to the surrounding air flow when driving.
Government regulations and pressure upon reducing fuel consumption has been the
main concern for automotive manufacturers in the last decade, creating a tendency
when the main aim is reducing the aerodynamic drag of ground vehicles. The flow
around a vehicle is responsible, not only for the drag production, but also for its
directional stability and effective handling. Even though this is a recent tendency, as
early as 1986 studies like Gilhaus and Renn (1986) or Howell (1993) were already
predicting that streamlining vehicles to reduce drag tends to increase the crosswind
sensitivity.
As the interest of designing better-quality and more sophisticated vehicles increases,
so does then the attention to crosswinds and unsteady aerodynamics. Gust and
cross winds can affect the manoeuvrability in different ways, since they are
generated by many factors (natural winds, vehicle overtaking, crossing a bridge,
uneven terrain), which the automobile designers cannot determine properly. In these
situations, the flow surrounding the vehicle becomes asymmetric resulting in the
presence of forces and moments that alter the stability. If a vehicle is traveling at a
Analysis of steady aerodynamic 1/49 Bracho_12071817.docx V1
forces in crosswinds using a 20/09/2013
bicycle model and CFD 2013 © Oxford Brookes University Jose Javier Bracho

high speed and is exposed to crosswinds, a path deviation might be caused by these
forces, and this must require a reaction and proper adjustments by the driver. Since
wind dusts randomly occur in different strengths and directions, is very difficult for the
driver to react or anticipate the vehicle response under these effects.
Consequently, significant attention is been given lately to unsteady aerodynamic
forces generated by crosswinds and overtaking manoeuvres: Schroeck et al. (2011);
Gajendra et al. (2009) and Mayer et al. (2007) are just a few examples, since the
effects on vehicle safety is a real concern among the industry. According to
estimations done by Baker and Reynolds (1992), during January 1990, there were at
least 390 wind-related road accidents in England, of which 47 per cent involved
overturning, 19 per cent of these caused by course deviation. In overall statistic
terms, Kobayashi and Kitoh (1983) reported that 1.2 per cent of all accidents on the
Tohoku Expressway in Japan have been found to be related to cross winds. Though
it is a small number, is still significant if we extrapolate the effect to more highways
around the world.
It is clear that crosswind stability will still be a concern for the tomorrow’s vehicles.
There is no doubt that ground vehicles are constantly evolving and changing with a
closed marked motivated to produce edgy designs mostly focused in areas like
sustainability, economy of energy, passenger’s comfort and services are becoming
more important than pure performance. Current research show a strong focus on
lighter solutions for new vehicles, which enforced stronger needs for an improved
understanding of the coupling between crosswind stability, vehicle external shape
and the dynamic properties. Developing methods that would help control the
response of vehicles facing these conditions is desirable in any level of production.
The relevance and importance of these tools makes them a valuable asset to every
manufacture and automotive designer.
Generally, the problem of evaluating the crosswind sensitivity of a vehicle is that it
involves a combination of aerodynamics, vehicle dynamics and driver interactions to
a given disturbance. To estimate the crosswind directional stability, each of these
issues relates to a demanding problem on its own and is usually investigated
separately.

Aerodynamic studies have been focusing the attention to side wind disturbances in
many ways. Several methods exist to address the investigations of design alterations
to reduce the crosswind sensitivity of ground vehicles in steady and unsteady
conditions. Experimental investigations have been limited by the difficulty to
represent accurate and realistic crosswind conditions. The flexibility and practicality
of computational models allows the designers to manipulate parameters and evaluate
their effects faster, easier and cheaper. Also considering multiple and repetitive
scenarios which allow an accurate modelling and a more appropriate conceptual
design. But while the numerical methods provide more flexibility than testing
scenarios, the lack of accuracy for lower order methods and the large computational
times for advanced modelling also compromise this approach.
Vehicle dynamics response is asses experimentally by driving vehicles through fans
measuring lateral displacement and comparing different designs, while driver
reactions have also been investigated to find which mechanical component the driver
is the most sensitive to. The numerical simulations undertaken lack the proper
aerodynamic inputs so they tend to be not fully representative of the real life
scenario. The combination of tools that, not only allows calculation of aerodynamic
forces, but also describes in a dynamic way the effects on the vehicle stability is very
desirable and beneficial for the field. At the moment not many investigations deal with
the implementation of these two areas, but with the combination of CFD and vehicle
dynamics simulations a more effective coupling of these studies can be included in
the design process of future vehicles.
Main aim of the dissertation
Study the effects of steady aerodynamics and crosswind stability on road vehicles
using computational fluid and vehicle dynamic models. The impact of aerodynamic
forces and moments together with key vehicle dynamics properties on vehicle’s
manoeuvrability and handling will be considered for different body geometries,
exploring the parameters which influence the vehicle the most.

Objectives of the dissertation
• Develop a CFD model able to measure the aerodynamic forces and moments on
a basic passenger vehicle shapes under crosswind conditions.
• Develop a simple bicycle model to determine the influence of key vehicle dynamic
properties on vehicle manoeuvrability and crosswind sensitivity.
• Replicate different body geometries (notchback, hatchback and square-back) to
investigate the effect of each one on vehicle dynamic response, specifically yaw
rate and lateral deviation.
• Identify the geometry features and design parameters which influence vehicle
handling and stability under crosswind situations the most.
Outline of the dissertation
The structure of this project is as follows. First introductory chapter is presented with
key information and contextual matters in order to familiarize the reader with the
topics discussed. The literature review chapter describes all the precedent studies on
the subject describing, not only the findings and key aspects of the investigations, but
also some details about the justification and limitations of the methods considered
throughout this project. Third chapter deals specifically with these methods,
describing in detail the outline of each simulation and numerical method carried out,
giving proper explanation to each stage of the modelling. Main results and discussion
are given in the next chapter where trends and behaviours observed throughout the
simulations will be pointed out and proper analysis is given to each model. Final
chapter outlines the general conclusions giving a proper summary of all the findings
and most important outcomes of the project, along with future work proposals.

Chapter 2
LITERATURE REVIEW
This chapter presents the definitions, concepts, theoretical background and previous
studies that have been used to elaborate the ideas of this project. First section deals
with basic equations and definitions around ground vehicle aerodynamics, simple
concepts of Navier-Stokes equations, Reynolds number consideration, boundary
layers and definitions of forces and moments. All previous studies on crosswind
relevant to this project are reviewed in section 2.2. The definition of a crosswind
scenario is defined first. Secondly, the influence of basic car shapes on the general
properties of cars while in steady crosswind is analysed. Some examples of unsteady
crosswind testing investigations are given, even though the approach taken on this
project will deal only with the steady state situation. Analytical modelling and
numerical investigations previously performed are addressed in section 2.3 and
finally section 2.4 considers studies where vehicle dynamics is taken into account to
investigate crosswind sensibility of ground vehicles.
2.1 Ground vehicle aerodynamics
Incompressible Navier-Stroke (NS) equations define the flow around a ground
vehicle, due to the relatively low-speed considered:
𝜕𝑢𝑖
𝜕𝑡
+ 𝑢𝑗
𝜕𝑢𝑖
𝜕𝑥𝑗
= −
1
𝜌
𝜕𝑝
𝜕𝑥𝑖
+ 𝑣∇2
𝑢𝑖 𝑖 = 1,2,3
(2.1)
𝜕𝑢𝑖
𝜕𝑥𝑖
= 0 , (2.2)
where 𝑢𝑖 is the i-component of the velocity, 𝑥𝑖 the i-direction, 𝑡 the time, 𝑝 the
pressure, 𝑝 the density and 𝑣 the kinematic viscosity. Since the derivation of NS
equations begins with the application of Newtown’s second law (conservation of
momentum) written for an arbitrary portion of the fluid, Equation 2.1 is then the
momentum equation representing the advection of the flow while Equation 2.2 is the

continuity equation representing the conservation of mass. Reynolds (1883) related
the influence of the flow velocity, a characteristic length of the flow case and the
molecular viscosity while studying the flow through a channel. Different flow regimes
then can be described and classified using the so-called Reynolds number (𝑅𝑒):
𝑅𝑒 =
𝑈𝐿 𝑟𝑒𝑓
𝑣
, (2.3)
where, 𝑈 is the flow velocity, 𝐿 𝑟𝑒𝑓 is the characteristic or reference length of the
system (i.e. car length) and 𝑣 the kinematic viscosity.
According to Hucho (1998), ground vehicle aerodynamics involves different aspects
and applications of the NS equations. The 𝑅𝑒 numbers considered are fairly high. An
example from Favre (2011) is taken: for a car in the normal atmospheric conditions
traveling at 100 km/h, being 4.5m long (𝐿) and with a frontal area A of 2.09 m2
, the 𝑅𝑒
numbers are 𝑅𝑒√𝐴 ≈ 2.7 x 106
or 𝑅𝑒 𝐿 ≈ 8 x 106
. On the frontal part of the vehicle the
flow is first laminar with a transition occurring rapidly to a turbulent flow. A large
turbulent wake is formed due to the characteristic form of the base area for a typical
ground vehicle, also producing unsteady phenomena such as vortex shedding.
These represent fair challenges for the numerical simulations resulting in a
compromise between the complete representation of the physics and the numerical
resources to use.
Boundary layers
According to Barnard (2009) when flow passes through a vehicle the air appears to
stick to the surface, meaning that right next to the surface there is no measurable
relative motion as the viscosity becomes dominant. Individual molecules do not
actually stick to the surface, they move around randomly but their average velocity
component parallel to the surface is zero. The relative velocity of the air flow
increases rapidly with distance away from the surface, this layer formed is known as
the boundary layer. The thickness of the boundary layer thickness grows with
distance from the front of the vehicle, but does not exceeds more than a few
centimetres on a car traveling at normal open-road speeds. Despite its thinness, this
layer holds the key to understanding how air flows around a vehicle, as well as how

forces are generated. Firstly the boundary layer is laminar and after the flow has
reached a certain critical distance, it becomes turbulent. This transition is influenced
by a number of factors (displacement from leading edge, local pressure gradient,
etc.). Friction drag is larger in the turbulence boundary layer due to an increase
friction at the surface, opposed to the laminar case. However, the characteristics of
the boundary layer delay the separation location which will influence the aerodynamic
forces in a way. The boundary layer can be described using a non-dimensional wall
unit, 𝑦+
as:
𝑦+
=
𝑢 𝜏 𝑦
𝑣
, (2.4)
where 𝑢 𝜏 is the friction velocity and 𝑦 the normal distance to the surface. A full
representation of a boundary layer can be seen on Fig 2.1 where regions of laminar
and turbulent layer are clearly represented as well as a typical graph of velocity
against distance from the leading edge.
Figure 2.1: Boundary Layer on a flat plane (Cortana, 199?).
Aerodynamic forces and moments
When a vehicle is traveling in a fluid, the change of pressure around the body and
the friction of the flow of the vehicle surface generate aerodynamic forces. The
resultant of these forces are generally applied in a different place as the centre of
gravity, therefore aerodynamic moments are also present. Each component of
aerodynamic loads defines a type of force; refer to Fig 2.2 for a diagram. The drag

force is represented as the force acting in the stream wise direction (X), the side
force in the lateral direction (Y) and the lift in the upward vertical direction (L).
Moments are defined as: roll moment around the stream wise axis (R), yaw moment
around the vertical axis (N) and pitch moment around the lateral axis (M). The
reference frame used for the CFD models of this project is presented consequently in
Fig 2.3.
Figure 2.2: Vehicle aerodynamic forces and moments representation while
driving into a crosswind (Hucho and Emmelmann, 1973).
Non-dimensional coefficients can be defined for each force (𝐶 𝐹) and moments (𝐶 𝑀)
as:
𝐶 𝐹 =
𝐹
(0.5 ∗ 𝜌 ∗ 𝑈𝑟
2
∗ 𝐴) (2.5)
𝐶 𝑀 =
𝑀
(0.5 ∗ 𝜌 ∗ 𝑈𝑟
2
∗ 𝐴 ∗ 𝐿)
, (2.6)
where, 𝐹 is the force (i.e. drag, lift and side force), 𝑀 the moment (i.e. roll, pitch and
yaw), 𝜌 the density of air, 𝐴 the projected frontal area of the vehicle model and 𝑈𝑟 the
incident velocity considered (√𝑈2 + 𝑊2).

2.2 Previous studies on crosswind
Definition of crosswind scenario and quasi-steady behaviour
Crosswind, according to OED (2013) is defined as: a wind blowing across one’s
direction of travel; in this case, the vehicle’s direction of travel.
Figure 2.3: Reference frame used for the CFD models (taken from Favre, 2011).
Crosswind is represented by W in Fig 2.4. The resultant flow velocity is shown in this
example as the summation of the vehicle traveling speed, 𝑈; and the wind blowing at
90°, 𝑊. The wind can blow at different angles indeed, but the easiest way to
implement for testing and numerical studies is 90° wind angle. The yaw angle ψ is
the resultant angle of incidence with respect of the car’s traveling direction.
Figure 2.4: Resultant flow velocity in a crosswind situation.
The mathematical representation for an unsteady resultant wind is expressed as
(Sims-Williams, 2011):
𝐷𝑈��⃗𝑟𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡
𝐷𝑡
=
𝜕𝑈��⃗
𝜕𝑡
+
𝜕𝑊��⃗
𝜕𝑡
+ 𝑈
𝜕𝑊��⃗
𝜕𝑥
, (2.7)

where 𝑥 is the direction of travel. If a vehicle is traveling at constant speed ((𝜕𝑈��⃗)/
𝜕𝑡 = 0), the unsteady crosswind can be originated from either a time varying side
wind ((𝜕𝑊��⃗)/𝜕𝑡, weather, gusts, etc.) and/or from spatial variation due to obstacles in
the close surroundings ((𝜕𝑊��⃗)/𝜕𝑥, pillars, other vehicles, tunnels, etc.).
There have been numerous investigations assessing possible crosswind scenarios,
with different approaches. A most recent approach is the transient crosswind
situation, side winds are time dependant and the incidence of the forces build up to
steady state is studied as a fundamental part of the crosswind effects. To
characterize the extreme case of crosswind gust that a vehicle could encounter,
studies using on-road measurements were carried by Klasson (2001) and Wojciak et
al. (2010). In the last one, statistics of wind gusts were collected during high weather
conditions. With 63% of the collected data, single peak gust occurs the most and
trapeze peak in second with 28%, with wind speeds varying from 4 m/s (36% of the
collected data) up to 8 m/s. Length scales observed the most were around 20-40m
(around 4-10 typical vehicle lengths). In terms of stationary winds conditions (the
ones relevant to this project) studies like Wordley and Saunders (2008, 2009) help
characterize experimental equipment for on-road measurement finding
recommendations for simulating the turbulence encountered by cars in wind tunnels.
According to Hucho (1998), the most critical crosswind scenario involving a yaw
angle up to 20° are considered as the most critical for cars.
In order to distinguish the approaches for crosswinds, Fig 2.5 is presented, as a
result of Sims-Williams (2011) investigation on crosswind and transients. The
spectral energy of the surrounded turbulence was introduced and the different areas
in this spectrum were defined using the reduced frequency expressed as:
𝐾 =
2𝜋𝑓𝐿 𝑟𝑒𝑓
𝑈
, (2.8)
where, 𝑓 is the frequency (Hz), 𝐿 𝑟𝑒𝑓 the characteristic length (in this case vehicle
length) and 𝑈 the flow velocity. The spectrum then can be divided into quasi-steady
behaviour for K < 0.8 from the transient behaviour. The area of interest for this
project is precisely this quasi-steady behaviour with turbulence of length scales
around 30-300m and very low frequencies.

Figure 2.5: Division between quasi-steady and transient approaches for
crosswind (Sims-Williams, 2011).
In order to generate the low frequencies within a wind tunnel an active generation
system is needed, but this is a rather complicated and an uncommon process.
Examples can be seen in the Pininfarina facility and its turbulence generator system
(TGS), seen in Cogotti (2003).
Basic car shapes in steady crosswind conditions
Although many basic car configurations have been studied in steady crosswind
condition, two main investigations are worth noticing: Gilhaus and Renn (1986) and
Howell (1993), since they review a substantial amount of parameters. Gilhaus and
Renn (1986) evaluated the effects of various shape parameters on aerodynamic drag
and driving-stability related coefficients on a simplified 3/8-scale model with
interchangeable body parts.
Figure 2.6: Asymmetrical pressure distribution at yawed condition causing a
leeward steering effect (Gilhaus & Renn, 1986).

Finding that the absolute side force experience by the vehicle was not the main
problem, but more likely, the difference relating a stronger front side force compared
to the rear side force, resulting in a yaw moment which affects the steering, as seen
in Fig 2.6.
In Fig 2.7 a comparison of the yaw moment created by different vehicle shapes on
specific yaw angle is seen. The author’s explain that since looking at the basic
characteristics of yaw moment as function of yaw angle, for this range of car shapes,
a steady increase is seen up to a yaw angle of 20°; concluding that the coefficients
measured at this angle could provide meaningful to discuss the features investigated.
Figure 2.7: Steady increase of yaw moment within relevant range of yaw angle
(Gilhaus & Renn, 1986).
From this point it is very clear that changes in vehicle shape impact the side force
and yawing moment derivatives in different ways, and this is proved through many
other investigations such as: Yoshida, Muto and Imaizumi (1977), Klein and Hogue
(1980), Buchheim, Maretzke and Piatek (1985), Howell (1993). Although discrepancy
is found in some aspects; while it is generally acknowledged that station wagons or
squareback vehicles have a lower yaw moment than fastback and notchback
vehicles; Gilhaus and Renn (1986) found the notchback version to have a higher yaw
moment than the hatchback, while the opposite is described by Howell (1993).
Nevertheless, some parameters on both investigations are not well defined
suggesting that variations can apply within the same car family.
Other conclusions are found in these two main investigations relating changes in
vehicle geometry and yaw moment:

• If the overhang at the rear of a notchback car is increased this provokes an
increase in yaw moment.
• Increasing the radius of the C/D-pillars at the rear of any model tends to increase
the yaw moment.
• Increasing the radius of the A-pillars increases the yaw moment, however,
conclusions can be mistaken due to the iterative process used to address the
investigations.
Reader is encouraged to refer to Favre (2011) for more details about modification on
pillars radius and sharped edges, this project will deal with geometric alterations only
on rear shapes.
Unsteady crosswind experimental investigations
Regardless of the limitations and difficulties to develop accurate crosswind situations
and atmospheric boundary layers in testing facilities, a great number of investigations
and experiments have been developed. The majority of these are oscillating models
in which aerodynamic loads are measured. In an attempt to differentiate dynamic and
quasi-steady loads, Garry and Cooper (1986) used a simple truck model rotating it at
high yaw angles during the research; the results demonstrated a significant
difference between the two types of loads studied. However, Bearman and Mullarkey
(1994) carried out a series of wind tunnel testing in three different flow environments:
a uniform steam at various yaw angles, sinusoidal transverse gust superimposed on
a mean flow with wavelengths ranging between 2 and 20 model lengths and with a
peak gust angles up to ±8° and turbulent flows produced by grids. For the cases with
unsteady flows (gusts and grid turbulence) admittance functions were calculated
comparing forces and moments measured in the unsteady flows with values obtained
from steady situations assuming the flow around the vehicle behaves in a quasi-
steady way. The admittance values obtained were equal to unity or less suggesting
that, for the models tested, measuring steady forces and moments at fixed yaw
angles and assuming quasi-steady flow, leads to conservative estimates of unsteady
quantities. For all the models tested the side force and yawing moment coefficients
measured in steady flow exhibited nearly linear variations with changing yaw angle
up to 20°.

Other studies like Chometon et al., 2005, using a Willy model, concentrated in finding
the phase shift and hysteresis in the dynamic motions, while some, using production
cars, found that wake flow dominated the time-delayed observed. (Theissen et al.,
2011 and Wojciak et al., 2011). It is clear that these experimental studies are very
limited since there’s no real explanation or description of the physics involving the
delay or overshoot of aerodynamic loads.
2.3 Analytical modelling of crosswind and numerical investigations
Overview
Analytical methods have been analysed to understand the approximations and
limitations that they provide as techniques to calculate crosswind sensitivity. The
earliest description for aerodynamic derivatives prediction for automobiles was found
on Hucho and Emmelmann (1973); where, from an analytical and theoretical point of
view, a simple dynamic fluid model was developed by which the transient behaviour
of yawing moment and side force could be calculated when the profile of the cross
wind was known. The mathematical model used was borrowed from aircraft
aerodynamics but further validation was necessary. Probably the best description for
an analytical method is found in the set of papers by Baker (1991a,b,c) in which,
firstly, a dimensional analysis of the problem of ground vehicles in crosswind is
described, as well as flow patterns of vehicle shapes, calculated from steady
aerodynamic forces and moments; setting a framework to assess crosswind
situations and discussion on following parts and compiling data from a variety of
vehicle types in crosswind. Secondly, Baker (1991b) considers the unsteady
aerodynamic forces in the frequency, amplitude and time domains and sets them in a
consistent analytical context; introducing a term called aerodynamic admittance to
calculate unsteady loads due to high crosswinds. Aerodynamic admittance is defined
as the correction factor for the quasi-steady or ideal expressions, exposed in this
investigation, which assumes that force fluctuations follow velocity fluctuations
without attenuation or lag. Although some limitations were found on these analytical
methods, they set a solid background for further investigations including dynamic
models dealing with crosswind sensibility of rail vehicles.

Regarding numerical simulation there are a significant number of choices regarding
turbulence models to simulate aerodynamic flows. Solutions like Direct Numerical
Simulation (DNS) and Large-Eddy Simulations (LES) are very demanding in terms of
computational power for high Re number flow, and they will not be considered for this
investigation. The Reynolds-Averaged Navier-Stokes (RANS) equations discriminate
mean flow and fluctuations, generating a new set of equations called Reynolds
stresses which are modelled within the simulation. The strategies and hypothesis
taken to calculate these stresses will vary resulting in different types of RANS
models. The most common model within industry is the linear eddy viscosity model,
which is considerate to be questionable when transient flows are present (highly
turbulent flows, mixing layers, wakes, unsteady crosswinds, etc.) There are also
hybrid methods like Detached-Eddy Simulations (DES), combining LES in separated
flow regions and RANS in boundary layers. They have the advantage to lower the
computational cost allowing high Re numbers to be simulated.
Since this investigation will deal with steady state approaches, RANS linear eddy
viscosity models will satisfy the modelling demands. There are several subcategories
for the linear eddy-viscosity models, depending on the number of (transport)
equations solved to compute the eddy viscosity coefficient. Two-equation models are
the most common type of turbulence models. Industry standards k-epsilon model and
k-omega model are used for most types of engineering problems. By definition, two
equation models include two extra transport equations to represent the turbulent
properties of the flow. This allows a two equation model to account for history effects
like convection and diffusion of turbulent energy. This models also count with
distinguish near-wall treatment for low Re numbers and high Re numbers.
Steady crosswind
Some examples of numerical investigations of crosswinds, focused on steady
conditions, can be seen on Hemida et al. (2005), Diedrich (2006) and Bocciolone et
al. (2008), but their focus is mostly on rails. Gajendra et al. (2009) used a standard k-
epsilon turbulence model to simulate crosswinds of different speed and angle on a
typical sedan-type automobile, measuring the effects on aerodynamic coefficients.
Flow distribution around the car becomes heavily influenced by the yaw angle of the
incident crosswind, moving the stagnation point towards the windward side and also

affecting the vortices at the rear becoming asymmetric; therefore vehicle stability,
based on lift coefficient yaw moment values, is found to be poor at lower vehicle
speed and higher crosswind angles. Another example is Wojciak et al. (2012) where
the capability of an open source CFD software is analysed for unsteady vehicle
aerodynamics. Lastly, a comparison between performances of DES and RANS
models when simulating crosswind for several yaw angles in a Willy model was
undertaken by Guilmineau et al. (2011), concluding that improved results were
obtained for DES simulations particularly for large yaw angles, although with a
significant increase in computational sources and simulation time; around 4200h of
CPU time were necessary to run the RANS simulations with a very fine mesh,
composed by about 20M nodes; while 5000h were needed for DES computations.
Concerning the distinction between steady and dynamic analysis, Xinke Mu (2011)
evaluated a case with truck models on CFD simulations finding significant differences
between the load types, mainly in the wake behind the trailer and the pressure
coefficient. Shown in Fig 2.8, at dynamic condition the wake shifts to adjust to the
direction of rotation compared to that at steady condition. Author express that this is
due to the separation of the flow on the lateral surface at windward side occurs
earlier, while on the leeward side it is retarded.
Figure 2.8: Isosurface of total pressure at 1.6 degree yaw angle (Xinke Mu,
2011).
Pressure coefficient values at dynamic conditions show that the pressure on the
windward side is increased with respect to the static case, while the pressure on the

leeward side is decreased, leading to a drag reduction as well as a yaw-moment
reduction. Difference is clearly shown in Fig 2.9.
Figure 2.9: Pressure coefficient at the windward lateral surface of the trailer
(Xinke Mu, 2011).
2.4 Crosswind sensitivity
Yaw rate or yaw velocity is considered the key factor for handling and vehicle
stability, a sudden change in this parameter may result in a course change or
misdirection which could lead to traffic collisions. Baker (1986) considers the
rotational stability as the only concern for passenger car safety.
The relations between vehicle design and vehicle dynamics response regarding
crosswinds has been tested experimentally over the years with several methods,
where lateral deviations are compared between different designs. When studying the
crosswind sensitivity authors like MacAdam et al. (1990) have concluded that centre
of pressure of the aerodynamic forces has a major impact on the stability of vehicles.
Within this investigation an analytical relation between three ‘points’: centre of gravity
(CoG), centre of pressure (CoP) and neutral-steer point (NSP) is provided to qualify
vehicles under crosswind conditions. It is imperative then, in order to study the
crosswind stability of ground vehicles, that these three points must be monitored and
further analysed to determine their overall influence.
This investigation is aimed to couple advanced aerodynamics (CFD) and vehicle
dynamics simulations. If a full coupled crosswind simulation is aimed, the overall

position of the vehicle due to aerodynamic disturbances at each time step is needed.
A static coupling on the other hand, involves an aerodynamic simulation on a static
vehicle exposed to an unsteady wind gust and the transient loads are the input to a
vehicle dynamics simulation in order to calculate the vehicle deviation from its
course. Another possibility is a quasi-static or quasi-steady coupling, when a set of
aerodynamic simulations on a static vehicle exposed to static winds with different
yaw angles is undertaken. A relation between the aerodynamic loads and the static
wind angles is obtained and incorporated into the vehicle dynamics simulation,
analysing the response of the vehicle for a particular yaw angle. This quasi-steady
approach is the one taken for this investigation, even though it’s been demonstrated
by some studies (i.e. Ericsson and Reding, 1988) that parameters such as the delay
in growth of the aerodynamic loads or the modification of the flow features would lead
to different aerodynamic loads than those derived from steady crosswind.
Several papers were found dealing with the coupling of aerodynamic simulations and
vehicle dynamics. Thomas et al. (2010) used a static method to relate the loads
obtained from DES simulations, which further ahead were simplified to quasi-steady
representations and lead to similar dynamic response. Tsubukora and Nakashima
(2010) managed to obtain a full dynamic coupling between LES and vehicle
dynamics for a truck subjected to a strong wind gust. Takagi (2006) carried out an
investigation on the two most significant transients experienced by a vehicle in
crosswind: the first transient caused by the impact of the cross wind starting from the
front of the body, and the second on the effect of the pressure building up to reach
steady state condition. Static aerodynamic forces were accommodated into the
integrated form of transient equations of motion for a step input (first transient) and a
ramp input (second transient), as the pressure coefficient map obtained from CFD of
a steady state flow analysis for a yaw case of 20 degrees was assumed to be similar
to the one in transient period.

Chapter 3
METHODOLOGY
This chapter reviews all methodology related to the procedures and guidelines
followed throughout this project. Section 3.1 will deal with the vehicles geometries
considered, their dimensions and key features. Details on the RANS simulations for
steady state crosswind will be given in section 3.2, discussing mesh parameters, size
domain and other numerical setups required. Also, in order to explain the case
considered in the investigation, the initial conditions: yaw angle, wind velocity and
vehicle velocity are given along with the criteria used to select the values. Section 3.3
is presented in order to outline the coupling and implementation of aerodynamic
forces into the bicycle model, and the parameters involved in the modelling of the
vehicle dynamics. Finally, section 3.4 will explain the procedure for the parameter
study proposed to address the evaluation of specific points influencing the crosswind
stability of a ground vehicle. Appendix 1 shows an overall flow diagram of the
methodology to clarify the linking of the two methods.
3.1 Vehicle models
The vehicle models selected for this study are the three major variations of the MIRA
Reference Car which are: notchback, fastback and square-back, at full scale (1:1) for
the aerodynamic simulations. These models are the most frequently used within
industry representing the most common passenger automobile shapes. The
advantage of using these models is that they represent a realistic shape at the same
time are simple enough to facilitate the modelling and simulations tasks. Table 3.1
along Fig 3.1 is given to show the dimensions of the model as taken from Carr and
Stapleford (1986). Three different rear ends are observed, A, B and C, representing
notchback (NB), fastback (FB) and square-back (SQ) respectably. Rear end D is the
pickup model and will not be considered on this investigation. Several investigations
have been carried out with this reference model. As an example Carr and Stapleford
(1986) studied the blockage correction on three different wind tunnels for all four
original versions of the MIRA reference car in 1:5, 1:4, 1:3 and 1:1 scales. Gaylard et

al. compared simulation results using Star-CD against full-scale data from MIRA wind
tunnel as a validation exercise, comparing forces, pressures and flow visualization.
Surfaces pressures were found to correlate well. It is shown that CFD results also
predicted similar trends to those found experimentally in drag and lift coefficients.
Drag was predicted within 2% although absolute prediction of lift was considerably
poorer while lift coefficients and pressure signatures away from the centre-line were
less reliable. These two investigations will be were used to validate CFD models for
this project.
Table 3.1: Dimensional details of the MIRA reference car models.
Feature
Dimension
(mm)
Feature
Dimension
(mm)
1 - Overall Length 4177 9 - Boot Length (Notch-Back) 762
2 - Overall Width 1625 10 - Front Overhang 560
3 - Overall Height 1420 11 - Canopy Height 508
4 - Wheelbase 2540 12 - Lower Body Height 708
5 - Track 1270 13 - Ground Clearance 204
6 - Bonnet Length 1055 14 - Rad. of Rounded Edges 152
7 - Front Canopy Length 1790 15 - Frontal Area, m2
1.838
8 - Rear-End Length 1320
Figure 3.1: Dimensions of MIRA reference car model (See also Table 3.1).

3.2 RANS simulations of steady state crosswind
Overview of turbulence model
Standard k-epsilon turbulence model was selected for the simulations in this project,
for the advantage of being one of the most common models in industry and previous
knowledge modelling aerodynamic flows with this method. A K-Epsilon turbulence
model is a two-equation model in which transport equations are solved for the
turbulent kinetic energy 𝑘 and its dissipation rate 𝜀. In order to resolve the viscous
sub-layer or boundary layer this method applies a so-called two-layer approach in
which the computation is divided into two layers. In the layer next to the wall, the
turbulent dissipation rate 𝜀 and the turbulent viscosity 𝜇 𝑡 are specified as functions of
wall distance. The values of 𝜀 specified in the near-wall layer are blended smoothly
with the values computed from solving the transport equation far from the wall. The
equation for the turbulent kinetic energy is solved in the entire flow.
Numerical setup
A considerable number of investigations were found which dealt with simulations of
crosswinds for ground vehicles, some of the parameters chosen for the CFD models
in this project are based on these previous studies. Starting from the flow domain, a
considerable size is needed in order to avoid blockage effects not only on the stream
wise direction but also in the cross wise direction. Flow domain used by Favre (2011)
was found to be suitable for this project since, in essence, the same geometry is
studied and the same conditions are aimed, although this author undertakes a DES
simulation on an unsteady crosswind situation. Fig 3.2 shows the outline of the flow
domain selected as well as the boundary conditions for each wall; one inlet, one
outlet and a moving floor to accurately simulate all the conditions. Dimensions of the
flow domain are based on the vehicle length 𝐿 and vehicle height ℎ as shown. The
size of this flow domain is well within the dimensions suggested by studies like Singh
(2003) and Axelsson et al. (1998) were the recommended domain size for
automotive aerodynamics calculations provides clearances of at least two and three
car lengths upstream, five car lengths downstream, and twice the car height
vertically.

Figure 3.2: Computational domain dimensions and boundary conditions (Favre,
2011).
All meshes were created with the meshing tool found in STAR-CCM+. A mesh
optimization process was evaluated using the work of Ahmad et al. (2010). In this
study a mesh optimization strategy is proposed examining the effect of different
mesh parameters based on mesh base size selection, comparison between full and
half car models and mesh optimization using statistical analysis. The study was
carried out using the MIRA Reference Car fast-back variant, so the results are
standardized to the same models of this project. The investigation also aimed to find
the optimum mesh size in order to reduce the simulation time and computational
resources. Results based on vehicle length 𝐿 are shown in Table 3.2 for which a
difference of only 0.23% was obtained compared to the wind tunnel experimental
values.
Table 3.2: Optimum mesh values for vehicle aerodynamics (Ahmad et al., 2010).
Mesh
base size
(mm)
Car surface
mesh size (mm)
Surface
growth
rate
No. of
prism
layers
Prism layer
thickness
(mm)
3.6% x 𝐿 0.36% x 𝐿 1.3 5 5
Although the study proposes a polyhedral mesh as the most optimum, through the
development of this project the trimmer model was giving more accurate results with
less computational power and simulation time. Therefore the type of mesh selected

consists of a trimmer mesh with a prism layer model. It is also specified that
volumetric control around the vehicle could consume more memory and time than
having a mesh with constant grow rate but, in order to evaluate the flow around the
vehicle effectively in a crosswind situation, a small volumetric control was introduced
around the car model. A visual detail of the mesh is given in Fig 3.3.
(a) Trimmer volumetric control (b) Closer look of prism layer
Figure 3.3: Visual detail of trimmer mesh, volumetric control and prism layer
selected.
Approximate 2.2M cells were characterised on each model, with simulation times of
around 6 hours for 5000 iterations in the university cluster with parallel processing of
16 cores.
Initial Conditions
The aim of this project was to evaluate the steady state aerodynamic forces and
moments, therefore, static modelling where a static vehicle is subjected to static
winds with a certain incident angle will be used. Confirmed from numerous
investigations, a yaw angle of 20° seems to be the critical point for a ground vehicle
in a crosswind situation. Wind tunnel measurements in many cars have confirmed
that yawing moment coefficient and side force coefficient increase linearly beyond
20°, hence if conclusions are derived for this situation it will cover most driving
conditions. The cases considered in this project are inspired in the CFD simulations
of Favre (2011) and Takagi (2006). The first consisted of a stream wise wind speed
of 27 m/s corresponding to a maximum crosswind speed of 9.8 m/s to satisfy the
previously 20° set yaw angle. While the second one was carried out with a 33.33 m/s
vehicle speed and a corresponding crosswind speed of 12.1 m/s. To set a common

ground between them a vehicle speed or stream wise wind speed of 30 m/s was
selected, for an equivalent 10.92 m/s crosswind speed and a 𝑅𝑒 𝐿 = 7 x 106
. The
vehicle geometry was yawed 20° with respect to the flow domain to fulfil this
conditions and a stream-wise velocity of approximately 31.9 m/s was set at the inlet.
3.3 Vehicle dynamics simulations of a simple bicycle model
General approach
Although many of the investigations reviewed explore time-dependant or transient
effects, a simple bicycle model is needed to address the steady approach of this
project. Talukdar and Kulkarni (2011) described in their investigation that a planar
rigid bicycle model is one of the most popular models used in vehicle dynamics to
study vehicle handling characteristics and designing steering control systems.
Figure 3.4: Conventional bicycle model (Talukdar and Kulkarni, 2011).
A schematic diagram (Fig 3.4) of the two-degree of freedom bicycle model is given,
staying that the two degrees of freedom are the lateral velocity of the centre 𝑣 of
gravity and the yaw rate 𝑟. OXY is the fixed reference frame while O′X′Y′ is a moving
reference frame attached to the centre of the gravity and is oriented as per the SAE
sign convention. The axis X′ points in the longitudinal direction while the axis Y′
points in the lateral direction. VA, VB and VCG are the velocities of point A, point B
and centre of gravity respectively, αr and αf are the rear and front tire slip angles, β is
the vehicle slip angle, δ is the steering angle, Fyr and Fyf are the lateral tire forces

and a and b are the distance of the front tire axle and the rear tire axle from the
centre of gravity, respectively.
The main assumptions made in formulating the conventional bicycle model are:
• The right and left slip angles for the left wheel and the right wheel for both the
front and rear axle are the same.
• The effect of vehicle roll is small.
• The chassis is modelled as a rigid beam.
• There is no longitudinal load transfer.
• Small angle approximations are valid.
• The longitudinal velocity is constant.
Aerodynamic forces and moments obtained from CFD simulations were transformed
to the CoG local reference frame of the vehicle dynamics model. The crosswind
forces and moments were introduced to the simulation at a specific time after the
model reaches static equilibrium, which takes between 2-3 s. In order to determine
the vehicle sensitivity to the crosswind situation the lateral displacement is measured.
Exposed previously by Huber (1940) the lateral deviation is a suitable parameter to
address vehicle sensitivity because indicates the level of driver correction demanded
for the car to remain stable. Nevertheless, numerous studies have confirmed the yaw
rate as the main indicator of vehicle crosswind sensitivity. Investigations like
MacAdam et al. (1990), Uffelmann (1986), Hucho (1998, Chap. 5, p. 272) and Juhlin
(2009, p. 47) describe the yaw rate to be the most influential measure when it comes
to both analysing the crosswind sensitivity and the most important for subjective
judgement of the sensitivity by test drivers. Both parameters are used to describe
each vehicle model.
Mass related parameters
Since the MIRA reference car models selected for the CFD studies only represent an
external geometrical shape, mass related parameters needed for vehicle dynamic
simulations were extracted from data obtained in Allen et al. (1992), effectively
choosing vehicles with similar external shape and approximate wheelbase for each

model type. Table 3.3 shows the vehicles models selected and their mass properties
as measured in the referenced investigation. Weight distribution is measured with
respect to the front axle of the vehicle.
Table 3.3: Vehicle models selected for mass related parameters.
MIRA Model Vehicle Model
Wheelbase
(mm)
Total
Weight
(kg)
Weight
Distribution
(%)
Moment of
Inertia in
Yaw (kg*m
2
)
Tyre
Size
Notchback BMW 320i 1981 2578.61 1093.16 54.61 1791.60
185/70
R13
Fastback Renault LeCar 1977 2417.10 814.20 60.15 985.80
145S
R14
Square-back
Volkswagen Vanagon
1987
2471.90 1478.71 53.02 2471.63
185S
R14
Tyres cornering stiffness
The lateral forces experienced on the wheels will be calculated based on the tyres
slip angle and the cornering stiffness value considered according to the vertical load
on each axle and tyre size and model. Firstly, a method of estimation of tyre
cornering stiffness from basic tyre information was used as extracted from Hewson
(2005); a simple mathematical model were certain assumptions are made to simplify
the calculations, yielding cornering stiffness values within about 30 per cent of the
actual measured values. After having set a baseline value, linear approximations
based on CoG location and horizontal load distribution will be implemented to
differentiate the front and rear tyres cornering stiffness. A more detail explanation of
these calculations is given in Appendix 2.
3.4 Parameter study
Concerning the evaluation of the previously mentioned geometrical points which
influence the most on crosswind sensitivity (CoG, CoP and NSP) a parameter study
is proposed in which each of these ‘points’ will be moved along their longitudinal
positions to determine their overall influence on the yaw rate of each model. Centre
of gravity (CoG) longitudinal position is changed by moving the vehicle mass in
relation to the body and wheels. Aerodynamic longitudinal centre of pressure (CoP)
is moved by moving the body in relation to the CoG and wheels. And finally, the

neutral steer point is relocated by changing the tyres cornering stiffness combination
Monitoring the longitudinal positions of these three points it is possible to obtain a
simplified overview of the crosswind stability problem and therefore judge which of
these parameters is the most influential and how a compromise can be made, taking
into account other vehicle dynamics requirements, to improve crosswind response.

Chapter 4
RESULTS AND DISCUSSION
This chapter summarizes all the relevant results and findings obtained during the
investigation through different layouts, plots and tables. In section 4.1, CFD results
are shown first, where mainly pressure and velocity plots along with net values of
aerodynamic forces and moments are used to describe and discuss the particularities
observed in each model. Validation of CFD models is presented in Appendix 3.
Outcomes of vehicle dynamics simulations are given afterwards in section 4.2 where
an analysis of the influence of general vehicle parameters is presented against
values of yaw rate and lateral displacement. Parameter study is carried out in section
4.3, were the three most influential points for a vehicle in crosswind are evaluated
determining their overall influence in vehicle stability.
4.1 Computational fluid dynamics results
Pressure and velocity plots
Isometric pressure contours, shown in Fig 4.1, all indicate a high pressure region in
the front-end windward side of the vehicle due to stagnation, slightly higher on the FB
model but gradually diminishing along the width of all the models in a similar matter.
Low pressure zones are observed in the front-end leeward edges, for all models due
to standing vortices, and rear-end windward edges in all but SB due to its distinctive
shape which doesn’t allow trailing vortices to develop as the others do. There’s a
general from of asymmetry in which significantly higher pressures are observed in the
windward side of the models compared to the leeward side which also contributes to
the inequality of the low pressure zones and the spread displayed in the front-end.
Moreover these uneven pressure zones effectively exhibit an unbalance on
aerodynamic forces and moments along the length and width of the models.
Pressure contours around the vehicle, shown in Fig 4.2, demonstrate that the high
pressure zone windward side extends longer for the SB geometry, which could

explain a higher side force, and a low pressure zone leeward that prolongs further to
the rear-end clearly showing a bigger area for this specific model as well. The net
values showed that for FB and NB lower pressure values with respect to SB were
found on the front-end leeward side that could indicate a higher yawing moment.
Figure 4.1: Isometric pressure plots for FB, NB and SB models.

The same asymmetry with respect to the centre line of the car is observed and higher
low pressure zones on the rear indicate that drag forces will tend to increase with
respect to baseline. Variation on the location of the centre of pressure for each model
could be explained by analysing these plots; the further the high pressure zone
extends toward the length of the vehicle the closer the CoP of the side force will be to
the centre of the wheelbase.
Figure 4.2: Pressure distribution around the FB, NB and SB models.
FB
NB
SB

Figure 4.3: Velocity magnitude around the FB, NB and SB models.
Analysing the flow structure around the vehicle, Fig 4.3 shows the velocity
magnitudes for the three models. A low speed turbulence structure is observed at the
wake behind each model, with a noticeable difference in the number and size of
swirls developed by numerous factors. For the FB, the flow accelerating along the
roof and boot converges with the flow coming from underneath, extended to a larger
area due to the small diffuser. A single small swirl is present at the rear-end which
extends and creates another two swirls increasing the turbulence and the drag, due
to the uneven yawed condition that creates different flow velocities from the sides. A
similar behaviour is observed in the NB model although, due to the break observed in
the boot geometry, the flow tends to detach and separates more creating a bigger
swirl which explains a higher drag for this model. In the SB case, the flow travels all
the way to the rear-end of the vehicle without any sudden acceleration caused by
geometry alterations and, due to a bigger flow separation caused by the rear shape,

two swirls are created from the two incoming flows which again extend further and
converge into a big swirl due to the yawed condition; further increasing the drag.
Aerodynamic forces and moments net values
Table 4.1 laid out aerodynamic forces and moments net values. Drag force
experienced an increase of around 16% for all models with respect to baseline
values, which agrees with the range observed in Nguyen, Saunders and Watkins
(1997) for similar vehicle geometries at 20 degrees yaw angle also taking into
consideration that sharped-edged models at large yaw angles tend to experience
bigger changes in drag when compared to more aerodynamic models, as exposed in
this same paper, due to a slight increase in turbulence. The previously explained flow
structures also contribute to the explanation of this increment. For the lift, an
increment is greatly noticeable since baseline models were found to experience
some source of downforce and yawed cases all turned into positive lift values. The
overall flow redistribution around the car with the introduction of crosswind is said to
be the responsible for this variations as stated in Gajendra et al. (2009).
Table 4.1: Aerodynamic forces and moments net values.
Model
Drag
Force (N)
Lift Force
(N)
Side Force
(N)
Yawing
Moment* (N*m)
Notchback 417.36 878.50 823.60 643.78
Fastback 310.74 951.79 784.95 759.44
Square-back 484.02 560.09 1246.64 317.63
*measured from the wheelbase centre.
The position of the side CoP can be determined from dividing the yawing moment
obtained by the side force; this will give a reference point with respect to the
wheelbase centre in which the line of action of the side force is located. The divisions
of these values in Table 4.1 showed that FB centre of pressure was forward from the
wheelbase by 18% of vehicle length, NB was found to be 16% of vehicle length,
whereas SB was 8% of vehicle length. The distribution of the side area of the car
effectively influences the position of the side force CoP, therefore the yawing
response is sensitive to the body style: SB geometry with more area concentrated to
the rear experiences lower yawing moments than NB and FB while side force has
increases with side area. Rounding on the rear corners was also found as a styling

aspect with increases yawing moment, although having a beneficial effect on drag;
this could also contribute to the differences observed since FB and NB both count
with rounded rear corners, as opposed to SB. In general, the main source of
problems related to yawning stability is the rear-end of the vehicle as demonstrated
by this results and studies like Gilhaus and Renn (1986) were modifications were
also made to the front-end of the models finding that they were not as noteworthy.
4.2 Vehicle dynamics results
For the vehicle dynamics simulations the results obtained in the CFD modelling were
extrapolated to fit the bicycle model proposed. In some regards, approximations
based on results found were used in order to accurately and effectively include all the
conditions observed in the aerodynamics simulations. Lift force, for example, was
included as a force acting in the CoG of the vehicle’s, since for all the models pitching
moment around this point was found to be very small, therefore not affecting in a
reasonable matter the weight distribution for the yawed case. Hence, total weight was
calculated from:
𝑊𝑇 = 𝑊𝑐𝑎𝑟 + 𝑊𝑑𝑟𝑖𝑣𝑒𝑟 − 𝐿 𝑓 (4.1)
where, 𝑊𝑐𝑎𝑟 is the specific weight of the vehicle as taken from Table 3.3, 𝑊𝑑𝑟𝑖𝑣𝑒𝑟 is
the specific weight of the driver, taken as 80 kg; and 𝐿 𝑓 is the calculated aerodynamic
lift force in kilograms taken from Table 4.1.
The nature of the bicycle model rules out any inclusion of rolling moment to the
dynamic simulations, further work to be taken into consideration could include the full
aerodynamic conditions for a vehicle in yawed condition, consisting of a full vehicle
model with seven degrees-of-freedom and a dynamic tyre model able to calculate
cornering stiffness and lateral forces based on the vertical load variations due to roll
and pitch moments.

Crosswind stability
To address the analysis of stability and manoeuvrability two parameters were
measured in the dynamic models: yaw rate and lateral displacement, plotted in Fig
4.4 and Fig 4.5 respectively.
Figure 4.4: Yaw rate for the FB, NB and SB models.
Figure 4.5: Lateral displacement for the FB, NB and SB models.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
1.50 2.00 2.50 3.00 3.50 4.00 4.50
YawVelocity(rad/sec)
Time (sec)
FB NB SB
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
1.50 2.00 2.50 3.00 3.50 4.00 4.50
LateralDisplacement(m)
Time (sec)
FB NB SB

Validation of these results comes from the work seen in Favre (2011), where the SB
model was exposed to a gust of 9.8 m/s for 3 seconds while traveling at 27 m/s.
Unsteady aerodynamic modelling and a seven degree-of-freedom dynamics model
were used in this thesis, finding that at the peak of the gust SB geometry showed a
yaw rate of 0.03 rad/sec and a total lateral displacement of 2 meters by the end of the
simulations, effectively agreeing with the results obtained in this project. Another
source of comparison comes from Takagi (2006), where CFD results coupled to a
bicycle model of an unspecified geometry were analysed by introducing a step and a
ramp input into the dynamics modelling. As for the step input an overshoot of around
3 deg/sec (0.05 rad/sec) was present the in the first 0.5 seconds of the simulation,
like showed in this case for the FB model.
At first hand, the results show that FB model is significantly more unstable in the
crosswind situation proposed than the other two geometries, but not mainly due to
aerodynamic properties. Although having a CoP with a further distance from the
wheelbase centre than the two other models and a midway side force net value, the
key aspects that make the FB model the most unstable are seen in the vehicle
dynamics parameters: a lower moment of inertia, the smallest tyres and a weight
distribution almost 6% higher to the front axle than the other models. Adding all these
conditions makes this vehicle react poorly in a crosswind situation.
In terms of the other two models, SB is seen as the most stable, with nearly 50% less
maximum yaw rate and a total lateral deviation of 2.5 meters compared to 6 meters
obtained for the NB model. It is crucial to point out that these measurements are only
a relative comparison on how the models will behave when hit by a wind guts and
does not, by any means, suggest that the vehicles will actually drift away from their
steady path by this amount of lateral deviation. In order to correctly address this
matter a closed-loop system must be included, where driver’s reactions are taken into
consideration. The study of these conditions is critically sensitive to the steering and
responses of the driver. Other factors related to suspension geometry not taken into
consideration could also affect these values (i.e. steering caster effect). For a more
clear comparison Fig 4.6 shows the difference between a lateral deviation with a free
steering wheel, a desired response and an overcorrection from the driver.

In order to resist a side force, the tyres have to adopt a slip angle relative to the
direction of motion implying that, to maintain a steady path, the vehicle needs to be
yawed slightly towards the wind gust direction. A short delay is taken into
consideration for the reaction time of the driver and, after a steering input begins to
be applied, a further delay occurs as the springiness in the mechanical system is
taken up. Course deviation then starts to decline and in the desired response the
vehicle goes back to its original path. Time and distance taken to return to the line
and the deviation reflex both vehicle’s stability and driver’s skills. Hence, this data
gives a broad idea on how quick or sharp driver’s reactions must be; since a steeper
response observed on the free steering wheel case demands quicker reaction times
and bigger steering responses from the driver, although an element of subjectivity is
always present.
Figure 4.6: Driver controlled and stable reaction compared to natural unstable
mechanical responses of a vehicle to a sudden side gust (Emmelmann, 1987).
Many other factors can affect the perception of these results. Driving position can
also influence the stability of the vehicle/driver system: in a forward-control vehicle
the driver will be exposed to greater lateral accelerations compared to sitting near the
CoG, and may therefore react more quickly. Effectively, the aerodynamic stability
effects cannot be separated from the characteristics of the suspension, steering and
driver reaction, needing extremely complex full mathematical analysis to impeccably
address road vehicle dynamics in crosswind situations.

4.3 Parameter study results
Parameter study was carried out and results are shown in Table 4.2 where data from
the FB model was used. The principal parameters deifying lateral stability in a
crosswind situation using a simplified static analysis are the longitudinal positions of:
centre of gravity, centre of pressure and neutral steering point. The values of the
parameters influencing the position of these three points are varied and the changes
in yaw are analysed. Positions are relative to the front axle. Cornering stiffness (CS)
difference refers to the absolute difference between the front and the rear tyres.
Table 4.2: Test matrix and parameter study for the FB model.
Case
CoG
Rel.
Position
(mm)
CoP Rel.
Position
(mm)
NSP Rel.
Position
(mm)
Max Yaw
Rate
1. Baseline 1170.43 507.64 1181.31 1.00
2. CoG Forward (+10%WD) 912.57 507.64 1181.31 0.64
3. CoG Rearward (-5%WD) 1299.36 507.64 1181.31 3.21
4. CoP Forward (+20%) 1170.43 375.09 1181.31 1.25
5. CoP Rearward (-20%) 1170.43 640.20 1181.31 0.80
6. CS Diff 20% 1170.43 507.64 1142.39 1.27
7. Equal CS 1170.43 507.64 1289.30 0.75
8. CS Diff -15% 1170.43 507.64 1376.70 0.68
9. CS Diff -20% 1170.43 507.64 1404.07 0.66
As observed moving the CoG had quite an impact on yaw rate with the highest value
of yaw rate in relation to the baseline when moved rearward. NSP was also highly
influential especially when the cornering stiffness at the front was relatively higher
than at the rear wheels. As a general rule, when the NSP was located forward to the
CoG as in cases #3 and #6, the yaw rate showed the highest values, due to the fact
that the vehicle now will tend to over-steer when a side force is applied; the
resistance or damping effect of the vehicle due to its inertia is lowered and this
influences in a great matter. The opposite is valid for cases #2, 7, 8 and 9.

Although in reality these two points, CoG and NSP, cannot be moved without altering
the overall vehicle dynamic properties; by being linked to other vehicle dynamic
requirements they are limited in the possibility to move relatively to each other. Then
it’s the case of the CoP location. It is seen that it has a major influence on crosswind
sensitivity, as the point where the car experiences the side force is moved towards
the CoG, the yaw rate experienced decreases almost linearly in this model. Other
studies like MacAdam et al. (1990) and Alexandridis et al. (1979) have already
established this conclusion, meaning that this point is the primary key to address the
crosswind stability of a vehicle effectively if other dynamic properties are to stay the
same or ruled by other factors that cannot be modified. Although Favre (2011) also
points out that, with active or passive compliances, NSP position can be made more
dynamic or even event related in order to improve crosswind stability.
In order to have a vehicle not sensitive to the crosswind, a careful design of the
interactions of the dynamic CoP and NPS movements can develop a vehicle that at
first yaws at the same angle into the wind as the tyres need for slip angle to counter
the lateral force of the steady state wind gust; effectively giving a straight line vehicle
response which requires no correction from the driver. The requirements to make this
possible are that the CoG has to be slightly in front of the CoP on crosswind entry
and the CoP and NPS have to be closed together in the steady state.
Figure 4.7: Lateral displacement improvement after applying the balancing of
parameters (Favre, 2011).

Also in Favre (2011), an example of these method put into practice was made when
the vehicle geometry with the largest lateral deviation and highest yaw rate was
modified following the previously explained approach. The first step was to move the
body rearwards behind and in the vicinity of the CoG op to a level when the rest of
the yaw rate can be changed by varying characteristics of bushing and tyres to move
the NSP forward but still behind the CoP. This compromise shows the required levels
to reach for the CoP and NSP positions to achieve a balanced yaw response and
reduced lateral deviation of the previously unchanged vehicle. A small lateral
deviation remains effect of a slip in the car due to the lateral force from the
crosswind. Results of this study are shown in Figure 4.7 efficiently showing that the
vehicle became stable during the wind gust when the modifications were made.

Chapter 5
CONCLUSIONS AND FURTHER WORK
The main findings and outcomes during the course of the investigation are described
below, containing the discussion of the main results and the definition of behaviours
and trends observed.
The general asymmetry observed in the pressure plots within the vehicle surface and
the area around it demonstrate that, for a crosswind situation, the car experiments an
inequality of forces and flow structures causing it to experience a significant yaw
moment due to a side force located in the front-end windward side. The location of
this side force will greatly depend on the side area of the vehicle as demonstrated by
the differences observed between the three geometries studies. In a general matter,
the more the area is distributed at the rear of the vehicle the less yaw moment this
will experiment, making the SB geometry have the lowest values indicating a closer
distance between the line of action of the side force (CoP) and the wheelbase centre.
In terms of stability, the FB geometry was found to be the most sensitive to
crosswinds, not only due to larger aerodynamic forces, but mainly due to a lower
moment of inertia, small tyres and higher weight distribution to the front axle.
Confirming that vehicle dynamics properties are strongly linked with aerodynamics
ones when it comes to analyse the crosswind sensitivity of a vehicle.
Addressing the analysis of key points when discussing crosswind stability, CoP
position was found to be the most influential, since CoG and NSP are intrinsically
linked to each other and cannot be changed freely without altering any other dynamic
properties. A compromise must be made to design the interactions between CoP and
NSP in order to develop a vehicle less sensitive to a possible side wind gust. Ideally,
to counter the lateral force of the steady state wind gust, the vehicle will first yaw at
the same ingle into the wind as the tyres need for slip angle, balancing the forces and
giving a close to straight line response with no correction from the driver.

Further considerations of dynamic models where tyre models include a systematic
calculation of cornering stiffness depending on vertical load will improve the results
obtained. This will allow the introduction of unsteady forces, which will change with
respect to time and couple accordingly, while the dynamics model will allow the
positioning of the three key points to vary in terms of the forces values and all the
other vehicle parameters alterations observed while in a crosswind situation.
Although other studies reviewed in this project included this type of seven degree-of-
freedom dynamic models, they only studied a single vehicle geometry and did not
carry out a comparison between different rear-ends or different vehicle geometries.
Other more complex geometries could also be used in order to determine the
influence of vehicle features such as: diffusers, spoilers, etc.

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APPENDICES

APPENDIX 1 - Overall diagram for the linking of CFD and vehicle dynamics
models.
Figure A.1: Diagram for the linking of CFD and vehicle dynamics models.
Major Inputs
 Vehicle Geometry
 Crosswind Situation
Major Outputs
 Lift Force
 Side Force
 CoP Location
CFD
Simulations
Vehicle Dynamics
Simulations
Major Outputs
 Yaw Rate
 Lateral Displacement
Major Inputs
 CoG Location
 Tyre Parameters
 Vehicle Mass Properties
Crosswind sensitivity
analysis and discussion

APPENDIX 2 - Cornering stiffness calculations.
The tyres cornering stiffness values introduced to the vehicle dynamics models were
calculated using the approximation in Hewson (2005). The simple mathematical
model used the following formula based on basic tyre information:
𝐶𝑆 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒 =
4𝐸𝑏𝑤3
3𝑥[2𝜋(𝑟 + 𝑤𝑎) − 𝐿]
(A.1)
where, 𝐸 is the belt compression modulus which is set to 27x106
N/m2
, 𝑏 is the
material thickness of the belt with a suggested value of 0.015 m for road tyres, 𝑤 is
the belt width, 𝑎 is the tyre aspect ratio, 𝑟 is the wheel radius; these last three can be
read off the sidewall of the tyre, and finally 𝐿 and 𝑥 are contact patch length and
pneumatic trail respectively which are not necessarily kwon but the paper defines
them as:
𝐿 = 2(𝑟 + 𝑤𝑎)sin �𝑎𝑐𝑜𝑠 �1 −
𝑠𝑤𝑎
𝑟 + 𝑤𝑎
��
(A.2)
𝑥 =
𝐿
6 (A.3)
More details on how the equations are found as well as the assumptions and
approximations on the general model are found on the actual paper by Hewson
(2005).
Baseline values of CS were found with formula A.1 and to account for the difference
in vertical load between the front and rear the following formulas were used:
𝐶𝑆𝑓𝑟𝑜𝑛𝑡 = 𝐶𝑆 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒 ∗ (1 + 𝐿𝑜𝑎𝑑 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 %/100) ∗ 𝑏/𝐿 (A.4)
𝐶𝑆𝑟𝑒𝑎𝑟 = 𝐶𝑆 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒 ∗ (1 − 𝐿𝑜𝑎𝑑 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 %/100) ∗ 𝑎/𝐿 (A.5)

APPENDIX 3 - CFD models validation.
Baseline (no crosswind) simulations were carried out in order to validate the methods
and parameters selected for the CFD simulations against known CD values obtained
in Carr and Stapleford (1986), where all three geometries selected for this project
were evaluated using a wind tunnel and blockage correction methods. Table A.1
shows the results obtained where CD values are compared between the wind tunnel
testing and the computer simulation carried out in this project.
Table A.1: CFD baseline models validation.
Model
Wind Tunnel
Value
CFD Value
Difference
(%)
Notchback 0.270 0.292 7.48
Fastback 0.315 0.317 0.73
Square-back 0.380 0.401 5.16
Results obtained are within an acceptable range, a maximum of 7% difference is
shown in the NB model but less than 1% in the FB case, making the methods and
simulations chosen acceptable and inside the tolerable error for this kind of
investigations.
END OF DOCUMENT

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