This document discusses vehicle testing and data analysis for aerodynamic parameters. It begins with introductions to key aerodynamic principles like drag, lift, and boundary layer separation. It then describes the methodology for simulator testing of different wing angles of attack. Results and analysis are presented on coefficients of drag, lift, and lap performance for varying setups. The document concludes with recommendations for wing parameters and directions for further work.
1. Vehicle Testing and Data Analysis
Benjamin Labrosse
BSc (Hons) Automotive Engineering
University of Wales Trinity Saint David
March 19, 2015
Lecturer: Tim Tudor
4. List of Figures
2.0.1.Effect of increasing normal load on lateral tyre force, [Katz, 2006] . . . . 10
2.0.2.Effects on cornering acceleration due to aerodynamic devices, [Katz, 2006] 11
2.1.3.A typical velocity/time graph produced by a coast down test . . . . . . . 12
2.2.4.A diagram showing the method of creation of lift of wings, [Glenn Re-
search Center, 2014] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.5.A typical graph produced from a constant velocity test . . . . . . . . . . 14
4.1.1.The calculated coefficient of drag of the car . . . . . . . . . . . . . . . . . 23
4.1.2.Rolling resistance of the car depending on the AoA of both wings . . . . 24
4.2.3.Coefficient of lift of both wings dependent of the wing setup . . . . . . . 25
4.2.4.Graph showing the wing stall of the front wing when the front wing is
kept at a constant AoA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.5.An x-y plot of lift versus velocity created in Pi Toolbox . . . . . . . . . . 27
4.3.6.A zoomed in section of the graph shown in Figure 4.3.5 . . . . . . . . . . 29
4.3.7.An x-y plot of lateral acceleration against speed . . . . . . . . . . . . . . 30
4.3.8.Screenshot showing the increased aero loads of setup F18R18 over F1R18
on the exit of Hatchet’s Hairpin . . . . . . . . . . . . . . . . . . . . . . . 31
4.3.9.A screenshot of drag and lift against distance, the top trace being drag
and bottom being lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3.10.Graph showing the driver lifting off the throttle (in the green box) between
Spitfires and Brooklands . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3.11.Graph showing the steering correction for setup F1R18 (red trace) . . . . 34
4.3.12.Plot showing the CoP of the car versus speed (bottom plot) and brake
and throttle position (top plot) . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.13.Graph showing the theoretical and actual steering percentage for a lap . 36
A.2.1.Boundary layer of an airfoil that has been exagerrated for demonstration
purposes, [John D. Anderson, 2005] . . . . . . . . . . . . . . . . . . . . . 43
4
5. A.2.2.Diagram showing the laminar and turbulent boundary layers, [de Haag,
n,d] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
A.2.3.Graph depicting the change of pressure over an airfoil with an angle of
attack of 0°, [John D. Anderson, 2005] . . . . . . . . . . . . . . . . . . . 44
5
6. List of Tables
1.1.1.Table showing the definition of the nomenclature used within this report 9
3.1.1.The different wing parameters tested in the simulator sessions . . . . . . 17
3.1.2.The various ride height setups used to investigate effect of ride height on
aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.3.The various rake parameters used in the simulator . . . . . . . . . . . . . 19
3.2.4.A list of the various maths channels created along with the corresponding
syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.5.A list of constants made in Pi . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.6.Table showing the different front and rear coefficients of lift for each setup 21
4.0.1.A table showing the driver feedback of each wing setup . . . . . . . . . . 22
4.3.2.A table showing the maximum and average speeds and maximum and
minimum lateral accelerations seen on track . . . . . . . . . . . . . . . . 28
4.3.3.Table comparing the theoretical steer percentage to the actual steer per-
centage on Hatchet’s hairpin . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.4.Table comparing the theoretical steer percentage to the actual steer per-
centage on Honda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.1.1.Table showing the lap time for each wing setup . . . . . . . . . . . . . . 39
6
7. Race car success is determined by the lap time produced; this is ultimately determined
by the ability of the car to grip to the surface. To increase the grip of the race car,
engineers must fully utilise the contact patch betwen the tyre and the road surface. To
do this, aerodynamic aids have been extensively used to increase the vertical loads on
the tyres simulating a heavier car without adding extra weight. This report identifies
some key aerodynamic principles that explain the mechanisms of lift and drag and how
they relate to a racecar. The report also includes some analysis of tests carried out in a
simulator based on the influence of varying wing parameters.
8. 1. Introduction
The use of aerodynamic components can change the driving characteristic of vehicles,
more important in the high performance sector. Aerodynamic demands vary throughout
the race season depending on the track being raced, leading to an easily changeable set
up being advantageous. If a race track is predominantly based on top speed and has few
corners then a lower downforce wold be beneficial to a track that has many turns and
no high speed sections. Having a good data acquisition engineer will allow a race team
to analyse data gathered from testing, be it track, wind tunnel or computational fluid
dynamics (CFD) and modify the setup accordingly.
This leads to the aim of this report. It is the aim of the author to effectively analyse
the data obtained from a series of sessions in the Base Performance Simulator. This
data will be used to analyse the effect that changing the angle of attack of both front
and rear wings has on the handling characteristic of the F3 race car being tested. A full
test procedure must be made to fully investigate the various aerodynamic parameters
available and directions for the driver written up.
Through the completion of this aim, the author will learn the fundamentals of aero-
dynamics and will learn the effects that various set ups has on the handling behaviour
of the car.
8
9. 1.1. Nomenclature
Symbol Definition Symbol Definition
L Lift CD Coefficient of drag
ρ Density of fluid CL Coefficient of lift
V∞ Flow velocity q∞ Fluid dynamic pressure
Γ Vortex strength S Wing planform area
p Pressure h Elevation
v Velocity D Drag
g Gravity
Table 1.1.1.: Table showing the definition of the nomenclature used within this report
9
10. 2. Aerodynamic Principles
The study of aerodynamics is more simply put, the study of the force and resulting
motion of air. This involves the effect of displacing air around an object and the prod-
uct of this alteration of movement. Air can only interact with an object if it applies
pressure. This means that aerodynamics could be the study of pressure on an object as
a consequence of movement of air. As an object moves through a fluid or air it collides
with molecules of air, this creates a pressure. The pressure creates a force that is always
perpendicular to the pressure, [Tudor, 2015].
In order to understand the effect that this pressure has on the object, Bernoulli’s
theorem must be examined:
p +
1
2
ρv2
+ ρgh = constant. (2.0.1)
Bernoulli’s theorem expresses that if pressure increases, the velocity must decrease
and the opposite is true if pressure decreases. The change in pressure created produces
drag and lift.
Figure 2.0.1.: Effect of increasing normal load on lateral tyre force, [Katz, 2006]
It is beneficial to the driver of the vehicle to increase the aerodynamic capability. This
is largely due to the increased cornering speed that can be achieved when aerodynamic
10
11. devices are added to the vehicle. The greater the vertical force seen on the wheels
of the car the greater the lateral force can be experienced prior to sliding, which can
be seen in Figure 2.0.1. This means that adding weight to the vehicle would allow
it to corner more quickly than if it had lesser weight. This added weight would also
add unwanted weight meaning that the vehicles acceleration and top speed would also
suffer. Using aerodynamics defeats the problem of added weight. Increasing the lift of
an aerodynamic device on a vehicle will have the same effect on cornering than adding
weight without adding physcial weight to the vehicle. Figure 2.0.2 shows the increase
in lateral acceleration achieved due to aerodynamic devices compared to cars without
aerodynamic downforce since the 1950’s.
Figure 2.0.2.: Effects on cornering acceleration due to aerodynamic devices, [Katz, 2006]
2.1. Drag
Drag is the aerodynamic resistive force and ultimately governs the top speed of high
performance race vehicles. It is largely produced by the pressure created by the frontal
area of the object colliding with air molecules. Other contributors are viscous effects such
as flow separation and skin friction, defined later in this paper. Drag can be calculated
by using Equation 2.1.2 expressed by John D. Anderson [2005].
11
12. D = q∞SCD (2.1.2)
If any of these entities are not known, or if it is to be calculated through testing, the
method outlined in Section 2.1.1 can be used.
2.1.1. Drag calculation
A method of defining the coefficient of drag of a vehicle is to complete a coast down test.
This involves driving the vehicle to high speed and then putting the vehicle into neutral
and allowing the car to keep going till it stops while going in a straight line. Once this
has been performed, a graph not dissimilar to that seen in Figure 2.1.3 should be seen.
This graph will enable the engineer to define both the coefficient of drag and the rolling
Figure 2.1.3.: A typical velocity/time graph produced by a coast down test
resistance of the vehicle. The gradient at the high speed end of the slope will give the
coefficient of drag and the bottom end will provide the rolling resistance.
By picking two points at each end of the line the engineer knows two values of ve-
locity and time providing a value for acceleration (note that it will be negative), see
Equations 2.1.3 and 2.1.5. The force that can be calculated, using this acceleration,
is the force slowing the vehicle down which is made of two components; the aerody-
namic drag and the rolling resistance. Solving Equations 2.1.4 and 2.1.6 simultaneously
will allow the engineer to define both the drag coefficient and the rolling resistance, see
Appendix B.
12
13. a1 =
∆v
∆t
=
v2 − v1
t2 − t1
(2.1.3)
F1 = ma1 = m(
v2 − v1
t2 − t1
) =
1
2
ρCdAv2
1 + RR (2.1.4)
a2 =
∆v
∆t
=
v4 − v3
t4 − t3
(2.1.5)
F2 = ma2 = m(
v4 − v3
t4 − t3
) =
1
2
ρCdAv2
2 + RR (2.1.6)
2.2. Longer path theory
The longer path theory defines the method in which lift is produced. There is a common
misconception that wing lift is created by the difference in velocities created either side of
the wing by the unequal distances. It is not the difference in velocities but the difference
in pressures. The pressure gradients are created by the changing velocities. According
to Bernoulli, if a gas speeds up then the pressure must decrease and the opposite can
be said if the gas slows down. A wing is shaped to to increase the velocity of the air
passing the wing by increasing the path the air must travel on one side of the wing. The
wing is then forced towards the lower gradient as high pressures always tend towards
low pressures, creating lift. This can be seen in Figure 2.2.4. Equation 2.2.7 is used to
Figure 2.2.4.: A diagram showing the method of creation of lift of wings, [Glenn Research
Center, 2014]
calculate the lift of a given airfoil and is expressed from John D. Anderson [2005].
13
14. L = q∞SCL (2.2.7)
2.2.1. Lift calculation
In order to find the coefficient of lift, the car must be subjected to a constant velocity
test. This involves the car being accelerated to a constant high speed so that the vehicle
is subject to significant aerodynamic forces. Once at the desired speed, the car is that
speed for a set period of time and then returned back to a stop. A coast down test can
be carried out in the deceleration phase. Figure 2.2.5 shows a graphical representation
Figure 2.2.5.: A typical graph produced from a constant velocity test
of a constant velocity test. The static phase is used to find the static loads on each
tyre which is then used as a parameter in the formulation of the coefficient of lift. At
any point, it is known whether acceleration, velocity and weight transfer are of positive
or negative magnitudes and this principle is used to derive the formulae for finding the
coefficient of lift. The mass of the vehicle is denoted by Ff for the front axle and Fr for
the rear axle. When the vehicle is static, it can be said the mass is equal to the static
loads on the tyres, that is,
14
15. Ff = Sf , (2.2.8)
Fr = Sr, (2.2.9)
where Sf and Sr denote the static loads of the front and rear axles respectively. When
the vehicle is in the acceleration phase it is subjected to aerodynamic forces and positive
weight transfer. This weight transfer will affect the aerodynamic properties due to the
changed angle of attack of the aerodynamic devices. This means the lift coefficient will
differ to when the vehicle is at constant velocity. The force on the axles when accelerating
is therefore defined as:
Ff = Sf +
1
2
ρCLf Av2
− WT, (2.2.10)
Fr = Sr +
1
2
ρCLrAv2
+ WT (2.2.11)
where CLf and CLr denotes the lift coefficient of the front and rear axles and WT is
the weight transfer. When the vehicle is in the constant velocity phase it is assumed
that only aerodynamic forces are affecting the forces on the axles with the forces being
denoted by:
Ff = Sf +
1
2
ρCLf Av2
, (2.2.12)
Fr = Sr +
1
2
ρCLrAv2
. (2.2.13)
In order to define the lift coefficient these equations must be rewritten with the lift
coefficient as the subject of the equation.
2.3. Balance
It is desirable for an engineer on a race team to know the balance of the race car and
the distribution of aerodynamic loads on the axles, that is, what percentage of the
aerodynamic loads are acting on each axle. This will change how the car handles with a
bias to the front of the vehicle causing it to be less stable at high speeds but providing
a greater initial turn in. A rear bias will make the car more stable at high speeds but
15
16. the car will tend to understeer. Driver feedback during the simulation tests will be used
to confirm these statements.
In order to calculate the bias, the centre of pressure (CoP) must be found:
FAF =
1
2
ρCLf Av2
(2.3.14)
RAF =
1
2
ρCLrAv2
(2.3.15)
where FAF is the front aerodynamic force and RAF is the rear aerodynamic force. The
CoP is then found using Equation 2.3.16. This equation provides a percentage from the
front axle at which the centre of pressure acts on. This means that a number less than
50 means there is a bias to the front axle and a number greater than 50 means the bias
tends towards the rear axle.
CoP =
FAF
FAF + RAF
× 100 (2.3.16)
2.4. Testing methods of aerodynamics
According to John Iley there are four main methods of testing for aerodynamics,
• Wind tunnel,
• Computational Fluid Dynamics (CFD),
• Track,
• Simulation,
stating that track testing is the most valuable method to use. He states that the other
three forms of testing do not provide as accurate results as testing on a track, although
simulation has become relatively close to track testing.
16
17. 3. Methodology
3.1. Simulator test process
The author was put with a group of four other students to carry out the test sessions.
Each member of the group was given a task to ensure the testing went efficiently. Two
members of the group were with the driver instructing him on what to do and to make
sure procedures were done consistently. One member was in charge of changing the
vehicle parameters at the end of every run. Another member was chosen to be scribe,
writing down the feedback provided by the driver on how the car handled. The final
member was in charge of checking the on screen data and organising the files being
recorded by the simulator.
Run # Front wing AoA (°) Rear wing AoA (°)
1 1 1
2 9 1
3 18 1
4 1 9
5 9 9
6 18 9
7 1 18
8 9 18
9 18 18
10 1 1
AoA = Angle of Attack
Table 3.1.1.: The different wing parameters tested in the simulator sessions
The simulator has 18 different angles available for each wing. It would be impossible
to test each angle due to time constraints in terms of simulator time and time available
to analyse the data. It was therefore decided to take three different wing parameters
for both front and rear wings; minimum, medium and maximum angles. This means
that nine different combinations are investigated. A tenth run will be completed on the
17
18. first parameter tested, this is to see how much quicker the driver completes the lap if at
all and will allow the author to incorporate this difference into his analysis. The wing
parameters being tested can be found in Table 3.1.1.
Table 3.1.2.: The various ride height setups used to investigate effect of ride height on
aerodynamics
Run Front ride height (mm) Rear ride height (mm)
1 20 40
2 22 42
3 24 44
4 26 46
5 28 48
6 30 50
7 20 40
Three different tests are completed on each parameter; a constant high speed (200kph)
run of approximately 20 seconds duration, a coast down test from 200kph and a three
lap run of Pembrey. The Pembrey tests consist of a warm up lap so that the driver
accustoms himself to the car setup followed by two consistent high speed laps.
It was also decided by the group to practically investigate the effect of ride height and
rake on aerodynamic handling. This meant two further test procedures were needed for
changing ride height and changing rake. Tables 3.1.2 and 3.1.3 show the parameters that
were inputed into the simulator car settings. It was decided to change the suspension
settings for both the ride height and rake tests by 2mm increments to increase the
accuracy of the results obtained. The same test procedure was adopted for the suspension
set ups as the wing set ups although different drivers were present for the aerodynamic
tests and the suspension tests. This may cause variations in driving style and ultimately
lap times.
3.2. Maths channels
Maths channels are used in Pi Toolbox to calculate entities that are not directly measured
from testing, for example, the degree of understeer or oversteer that a vehicle experiences.
Maths channels are therefore used extensively when analysing the performance of the
vehicle and driver in the data obtained. To make maths channels, a syntax needs to be
entered for the software to calculate the desired entity. Some maths channels are more
complicated than others, with conversions being the simplest. A list of maths channels
18
19. Table 3.1.3.: The various rake parameters used in the simulator
Run # Front ride height (mm) Rear ride height (mm) Rake (mm)
1 20 50 30
2 22 48 26
3 24 46 22
4 26 44 18
5 28 42 14
6 30 40 10
7 20 50 30
created by the author can be seen in Table 3.2.4 . Within the syntax of many maths
channels are entities titled CONST(x) with x being a constant. Constants are made
within Pi for values that are known to be constant throughout testing, for example, the
wheelbase of the vehicle. There is also an option to state if constants vary depending on
each lap. This is useful for things such as mass of the vehicle as this changes depending
on the amount of fuel that is in the tank. Table 3.2.6 shows the different coefficients of
lift for each setup that was put into Pi Toolbox to calculate the differing lifts for each
setup.
The maths channels are used to analyse the car performance. Two corners will be
analysed at Pembrey circuit; a low speed and a high speed corner. The low speed corner
is analysed to investigate the mechanical grip of the vehicle and the high speed corner
is analysed to investigate the aerodynamic grip. The low speed corner investigated is
called Hatchet’s Hairpin and the high speed corner is called Honda.
19
21. Table 3.2.5.: A list of constants made in Pi
Name Value Name Value
Air Density 1.223kg/m3
Gravity 9.81m/s2
CD 0.5166 Mass of vehicle (inclusive of fuel) 560kg
CL 2.009 Rear track 1.42m
Height of Centre of Gravity 0.23m Rear left static wheel load 1583N
Front left static wheel load 1160N Rear right static wheel load 1577.79N
Front right static wheel load 1166N Sprung mass of the vehicle 476kg
Front track 1.5m Wheelbase 2.73m
Frontal area 1.2m2
Table 3.2.6.: Table showing the different front and rear coefficients of lift for each setup
F1R1 F1R9 F1R18 F9R1 F9R9 F9R18 F18R1 F18R9 F18R18
CLF 1.5297 1.6503 1.6134 1.848 1.848 1.811 2.103 2.071 2.0342
CLR 1.753 2.235 2.535 2.194 2.494 1.882 2.148 2.447 2.4472
21
22. 4. Results and analysis
Table 4.0.1 shows the feedback given by the driver after completing the laps for each
wing setup. It shows that the car handled well and was best balanced when the front
and rear wings were set to the same angle of attack. When the wings are setup at either
extremity, that is, setups F1R18 and R18F1, the end with the greatest angle of attack
seemed to suffer.
Table 4.0.1.: A table showing the driver feedback of each wing setup
Wing setup Driver feedback
F1R1 Feels relatively balanced but lacking overall grip
F9R1 Oversteer especially at high speed
F18R1 Horrible, very poor rear end stability
F1R9 Back felt planted, suffering front end grip. More grip than previous runs
F9R9 Felt well balanced and provided good confidence
F18R9 Slightly loose rear but not too bad. Not front end limited anymore
F1R18 Horrible front end, definitely heading towards high speed understeer
F9R18 Tiny bit of understeer - more grip than previous setup
F18R18 My favourite setup - bit of front end oversteer but desirable
F1R1 Similar balance to previous run but less overall grip
4.1. Coefficient of drag and rolling resistance
Figure 4.1.1 shows the coefficient of drag of the car for each wing setup. It shows that as
the angle of attack of the rear wing increases the coefficient of drag also does. Another
trend found from the graph is that as the front angle of attack increases so does the
coefficient of drag. A reasoning that satisfies both of these trends can be drawn from
Equation 2.1.2. It states that the drag entity relies on the fluid pressure, the wing
planform area and the coefficient of drag of the wing. Each of these dependents are
constant during each test session. This means that if the coefficient of drag increases,
so must the drag from the wing.
22
23. Figure 4.1.1.: The calculated coefficient of drag of the car
For a race car, there are two major forces opposing motion, the first being aerodynamic
resistance and the second being rolling resistance. Rolling resistance is approximately
constant, only reducing slightly due to a reduction in mass from the reducing fuel mass;
it is assumed to be constant for this assignment. Figure 4.1.2 shows the rolling resistance
of the car on each wing set up. It follows the same trends as the coefficient of drag,
with the rolling resistance increasing as the angle of attack of both wings increases. The
variations are fairly insignificant however as the range varies over approximately 5N
from the highest to lowest rolling resistance. The rolling resistance is shown to be of a
negative magnitude as it is a retarding force; it is impossible to have a negative force.
4.2. Coefficient of lift
The values obtained for the lift and coefficient of lifts can be taken as negatives for a
car wing as the lift is not away from the ground but into the ground; the inverse to an
airplane wing. This means that an increasing coefficient of lift will result in a greater
downforce.
Figure 4.2.3 shows the coefficient of lift of both wings dependent on wing set up.
The first trend noticed on this graph is that as the rear wing AoA increases, the rear
23
24. Figure 4.1.2.: Rolling resistance of the car depending on the AoA of both wings
coefficient of lift increases; the same can be said of the front wing AoA. The relationship
of the interaction of both wings as the AoA increases is more complex. For the first
three runs, that is, with a constant front AoA of 1°, the coefficient of lift of the front
wing increases when the rear AoA increases but drops once the rear AoA goes beyond
9°. The author cannot state at which rear AoA this occurs as not enough tests have
been done. This may be demonstrating that the front wing has entered a stall situation;
the mechanism of which is mentioned in Section A.2.2. A close up of this stall is shown
in Figure 4.2.4. This reduction in coefficient of lift can be seen for front AoAs of 9° and
18°. Set up F18R1 shows an interesting situation; the front wing has a greater coefficient
of lift than the rear wing. It is the only set up for which this is true. Referring back
to Table 4.0.1, F18R1 appears to be the least confidence inspiring set up and the driver
stated that the car had a horrible front end. This is due to the lack of stability of the
car. As a huge aerodynamic load is felt on the front axle, the car becomes very twitchy
and sensitive to initial turn in.
24
25. Figure 4.2.3.: Coefficient of lift of both wings dependent of the wing setup
4.3. Lap analysis
Table 4.3.2 shows some statistics from each wing setup. This table can provide initial
feedback on the wing setups that provide better lap times. If the front AoA is kept
constant and only the rear is increased the maximum speed achieved during the three
laps decreases. This is countered with an increase in average speed; the difference in
maximum and average speed is approximately equal. It is more desirable to have an
elevated average speed than maximum speed. A greater average speed means that the
driver is negotiating corners with a greater speed and could also show a greater confidence
in the car.
If the AoA for front and rear wings are kept the same, that is, runs F1R1, F9R9
and F18R18, the same trend can be seen. The main difference between this trend and
the previous trend is that a much greater average speed is seen with both wings set
to maximum AoA compared to minimum AoA for a minimal compromise in maximum
speed. The greater average speed is due to the increased vertical loads on the tyres,
increasing the amount of grip available. This increased grip allows the driver to be more
confident and carry more speed through corners. This increased grip is also the reason
that the maximum speed is reduced; a greater grip results in a greater frictional force,
slowing the car down.
25
26. Figure 4.2.4.: Graph showing the wing stall of the front wing when the front wing is kept
at a constant AoA
4.3.1. Lift versus speed
Figure 4.3.5 demonstrates an x-y plot created in Pi Toolbox showing the total lift of
the car versus the velocity; the graph displays the lift for every wing set up. The graph
shows that the lift increases with velocity in a square law. It also shows that there is
only a small amount of variation of lift between each setup. A zoomed in section of the
lift versus velocity graph can be seen in Figure 4.3.6. It defines the difference between
each setup more accurately. At a velocity of 38m/s, it can be seen that the range from
the lowest lift to the greatest is only approximately 100N; this does not however show
the distribution from front to rear. The setup with the best lift on this graph may not
necessarily produce a fast lap time, if the distribution of lift is emphasised on one wing
the handling will not allow the car to be driven quickly.
4.3.2. Lateral acceleration versus speed
The author has decided to analyse the lateral acceleration versus speed graph for Hatchet’s
Hairpin and Honda to differentiate the mechanical grip to the aerodynamic grip. A graph
of lateral acceleration plotted against speed can show whether a car is cornering more
quickly or not. It is particularly useful in this application to compare capability of each
26
28. Table 4.3.2.: A table showing the maximum and average speeds and maximum and min-
imum lateral accelerations seen on track
Wing setup Max. speed Average speed Max. Accel Lat. Min. Accel Lat.
F1R1 66.94 43.22 5.24 -2.93
F1R9 66.11 45.59 2.74 -2.92
F1R18 65.77 45.96 2.82 -2.72
F9R1 66.37 42.80 2.73 -2.94
F9R9 66.67 47.01 2.96 -3.08
F9R18 65.66 47.06 2.96 -3.05
F18R1 64.67 36.21 2.36 -2.58
F18R9 66.15 45.55 2.98 -3.20
F18R18 65.92 47.58 3.02 -3.28
F1R1 66.85 46.28 2.75 -3.03
setup to corner at speed and will confirm the greater average speeds mentioned previ-
ously in Table 4.3.2. The whole graph can be seen in Figure 4.3.7 with the yellow boxes
showing the corners of interest in the yellow boxes and anomalous data in the green box.
The author will be analysing three aerodynamic setups, F1R18, F18R1 and F18R18, the
colour of the traces being red, grey and green respectively. This will hopefully show the
extremities of the aerodynamic capabilities of the car.
4.3.2.1. Hatchet’s Hairpin
Hatchet’s Hairpin is a tight hairpin resulting in the car cornering very slowly; this
means that aerodynamic effects will be minimal. The left hand box in Figure 4.3.7
shows the data for Hatchet’s Hairpin. The graph shows that all three setups have the
same minimum speed although different lateral accelerations are experienced. The red
and green traces follow more or less the same path although the green trace appears to
be earlier than the red; when the car is halfway between Hatchet’s Hairpin and Spitfires
the red trace reads 22.55m/s and 0.88G where the green trace reads 33.31m/s and 0.08G.
This indicates that the greater aerodynamic load on the front axle has allowed the driver
to exit the corner quicker than when very little aerodynamic load is present on setup
F1R18. This can be seen in Figure 4.3.8.
4.3.2.2. Honda
Honda is considered a quick corner on the Pembrey circuit; this means that aerodynamics
should play a large role in the cornering capabilities of the car. On the lateral acceleration
28
29. Figure 4.3.6.: A zoomed in section of the graph shown in Figure 4.3.5
graph it can be seen that the green trace is further to the right showing that the car was
able to corner more quickly when aerodynamic aids were present. The red trace shows
a velocity of 51.97m/s on the apex of the bend and a lateral acceleration of -2.51G, the
green trace has a velocity of 57.33m/s and a lateral acceleration of -2.34G at the same
point. This would explain an increased average velocity for the F18R18 setup mentioned
previously.
4.3.3. Drag and lift
Figure 4.3.9 shows the drag and lift traces produced for the three setups chosen for
one lap; the upper trace is the drag and the lower is the lift. The figure shows that
the general trace of lift and drag are the same with only the magnitude varying. The
figure shows that the red and grey traces are slower to enter the corners than the green
trace; this is shown by the delayed decrease in lift and drag. The major difference in
the shape of the trace lies between Spitfires and Brooklands. For both drag and lift,
the driver seems to be more planted with less fluctuations in velocity. This could be
showing a combination of increased driver confidence and an increase in grip. According
to Table 4.0.1, the driver was not confident with the setups producing the red and grey
29
31. Figure 4.3.8.: Screenshot showing the increased aero loads of setup F18R18 over F1R18
on the exit of Hatchet’s Hairpin
traces meaning that he would not be happy keeping the throttle at 100% around the
corners. This is shown if a throttle position trace is added to the plot, see Figure 4.3.10.
4.3.3.1. Hatchet’s Hairpin
On the entrance to Hatchet’s Hairpin, all three traces have nearly the same drag and lift
showing a variation of approximately 100N. This is proof that aerodynamic aids have
little effect when at low speeds due to the velocity squared rule. The braking appears to
be of the same force showing that the aerodynamic devices do not affect the retardation
of the car. When cornering, the green trace drops slightly lower than the two other
traces but appears to spend less time cornering. The car has taken 3.48 seconds to go
from 1000N of lift at the entrance of the corner to the exit for the green trace where it
takes 4.56 and 4.32 for the grey and red traces respectively. This shows that the higher
AoA of the wings on F18R18 allows the car to decelerate and accelerate out of the corner
at a greater rate. The setup F1R18 carries the greatest speed into the corner but the
driver does not seem confident accelerating out of the corner due to the double dip in
the corner. Adding traces for steer % shows that a correction was made at this point.
31
32. Figure 4.3.9.: A screenshot of drag and lift against distance, the top trace being drag
and bottom being lift
Adding the theoretical steer % shows that the driver is applying more steering than
is theorised meaning that the car is understeering. This would mean that the driver
would slow down to correct the understeer and apply more steer; this can be seen in
Figure 4.3.11.
4.3.3.2. Honda
When entering Honda, the grey trace is slightly lower than the other traces indicating
a lower entry speed to the corner. The grey trace shows a reduction of 700N over the
red trace and 200N of drag; this difference is caused by the different wing AoAs giving
the driver less confidence to go quickly. The F18R1 setup (grey trace) was said to have
a very poor rear end stability. This is due to the increased downforce on the front axle
making the front end twitchy and more likely to tend to oversteer.
The greatest difference in the traces is the exit values. The grey trace shows 780N
of drag compared to 1120N on the green trace and 830N on the red trace. A similar
difference is seen for lift with the green trace showing 1.5 times the lift of the grey trace.
This is once again influenced by the velocity carried out of the bend. The green is more
elevated due to the increased aerodynamic loads on the both axles creating a balanced
32
33. Figure 4.3.10.: Graph showing the driver lifting off the throttle (in the green box) be-
tween Spitfires and Brooklands
handling car. This increased aerodynamic load will increase the load on the contact
patch allowing the tyres to grip more to the surface, as seen in Figure 2.0.1. The greater
lift can be explained using the Kutta Joukowski theorem mentioned in Section A.1 as
the flow velocity is increasing.
4.3.4. Centre of pressure
The centre of pressure (CoP) channel shows at which point the CoP is acting upon the
car. The CoP is considered to be the point at which all the pressure forces acting on the
car are concentrated, [Barrowman, 1988], and is therefore represented as a percentage
from the front of the car, for example, a CoP of 48% determines that the majority of the
weight of the car is acting 48% from the front axle towards the rear. It is also stated by
Barrowman [1988] that if the CoP is behind the centre of gravity, the car will be more
stable. This inherently means that the car will be less stable if the CoP is in front of the
centre of gravity. The CoP versus speed plot is shown in Figure 4.3.12. If a polynomial
is inserted to the graph, it can be derived that a balanced car is roughly 46% from the
formula of the line (y = 0.000161444x + 45.4025).
33
34. Figure 4.3.11.: Graph showing the steering correction for setup F1R18 (red trace)
4.3.4.1. Hatchet’s Hairpin
Hatchet’s Hairpin is shown in Figure 4.3.12 as the box on the right hand side. The
graph shows that as the driver brakes to slow down for the corner, the centre of pressure
percentage increases. This is the opposite to the theory behind the channel. As the
driver brakes, the rake angle increases which sends the CoP further forward; this means
that a smaller number should be seen. This has led the author to believe that the CoP
is the percentage from the rear. The graph shows that as the car enters the corner and
applies the brakes, the CoP moves forward. The opposite can be said when exiting the
corner; the CoP moves backwards as the rake decreases. A spike can be seen before
the CoP returns to its normal range where acceleration is at it’s peak. The changes in
acceleration cause the change in CoP due to the longitudinal weight transfer that occurs.
4.3.4.2. Honda
Honda is shown as the left hand box in Figure 4.3.12. The CoP is similar to that of a
straight line section with a variation of approximately five percent indicating that very
little longitudinal weight transfer is occurring.
34
35. Figure 4.3.12.: Plot showing the CoP of the car versus speed (bottom plot) and brake
and throttle position (top plot)
4.3.5. Understeer and oversteer
Understeer and oversteer are the relation between the theoretical steer required to take
a corner of given radius at a given velocity compared to the actual steering input.
Understeer is the situation where the driver is having to input a greater steer than is
theorised and oversteer defines when the driver needs to put less steer in or in extreme
cases put an opposite lock on to straighten the car. To satisfy the question as to whether
a car is oversteering or understeering, the Ackermann steer angle must be defined; this is
done on a low speed corner to ensure that the car is balanced. It can also be defined in
terms of yaw rate. When the car is at Ackermann steering, it has a set yaw rate. When
a car is in oversteer, it is turning at a faster yaw rate than the steady state yaw rate and
when in understeer, the driver must increase the steer angle to catch up with the steady
state yaw rate. Figure 4.3.13 shows the theoretical and actual steering percentage, the
actual steer being the top trace; the left box shows Honda and the right shows Hatchet’s
Hairpin.
35
36. Figure 4.3.13.: Graph showing the theoretical and actual steering percentage for a lap
4.3.5.1. Hatchet’s Hairpin
Table 4.3.3 shows the theoretical steer and the actual steer input in terms of percentage.
It shows that all three setups are suffering from understeer as they are steering more
than calculated. The greatest understeering setup is F18R18 although the driver has
taken this corner differently for F18R18 than the two other setups. or F18R18 he has
“v’ed” the corner meaning a greater turn in angle but allowing the driver to get on the
power more quickly. This driving style tends to be apparent when the driver is more
aggressive. For the two other setups, the driver has taken a larger radius of turn. The
Table 4.3.3.: Table comparing the theoretical steer percentage to the actual steer per-
centage on Hatchet’s hairpin
Wing setup Theoretical steer % Actual steer %
F1R18 36.91 49.21
F18R1 43.72 50.46
F18R18 54.77 72
red trace shows that the driver has had to correct the steering angle to adjust for the
understeer. With the throttle position channel showing it can be seen that the driver
has also come off the throttle to assist the correction.
36
37. 4.3.5.2. Honda
Table 4.3.4 shows the theoretical steer and steer on Honda. It shows once again that all
three setups are in understeer going round the corner. The table shows that F1R18 is
in the greatest state of understeer with a difference of 18% followed by F18R18 and a
difference of 14%. A difference of only one percent is seen for setup F18R1. This is due
to the decreased velocity at which the car takes Honda as well as the increased vertical
loading on the front wheels, assisting the ability to turn into corners. The understeer
for F1R18 reflects with the driver feedback seen in Figure 4.0.1.
Table 4.3.4.: Table comparing the theoretical steer percentage to the actual steer per-
centage on Honda
Wing setup Theoretical steer % Actual steer %
F1R18 7.07 25.25
F18R1 6.32 7.57
F18R18 6.61 20.42
37
38. 5. Conclusion
Due to time constraints the author was not able to fully analyse the setups that were
tested; it was only feasible to analyse three out of the nine setups tested and only two
corners were analysed. This means that the conclusions brought together from the work
in this assignment may not be entirely accurate as a setting that was not tested may be
more suitable.
5.1. Wing parameter selection
It has been asked of the author to determine the most suited wing setup for a dry race.
This can be identified by observing the differing aerodynamic capabilities of each wing
setup and deciding which setup has the best properties to produce a quick lap with
minimal trade off in terms of drag. However, the author believes that the setup that
inspires the greatest confidence in the driver to push the car to the limits and produce
quick lap times would be the preferred setup for a race. The most aerodynamically sound
setup could be chosen but if the driver is not confident with the car then he will not
produce quick lap times. Table 5.1.1 shows the lap time for each wing setup. The setup
that produced the fastest time is F18R18 and according to Table 4.0.1 this setup proved
to be the favourite setup of the driver. This leads the author to conclude that this is
the best setup to be used according to the data that was collected for this assignment.
5.2. Further work
If the author had a more designated time in the simulator he would have conducted
more tests investigating more setups; in particular finding the point at which the wings
enter a stall siuation. The author did not have the time to investigate the effect of ride
height and rake in the analysis although the methodology has been shown in this paper
and the tests were conducted.
38
39. Table 5.1.1.: Table showing the lap time for each wing setup
Wing setup Lap time (seconds)
F1R1 47.647
F9R1 47.556
F18R1 51.237
F1R9 49.240
F9R9 47.920
F18R9 47.671
F1R18 49.056
F9R18 47.585
F18R18 47.120
39
40. Bibliography
Chenyuan Bai and ZIniu Wu. Generalized kutta-joukowski theorem for multi-vortex
and multi-airfoil flow (a lumped vortex model). Technical report, School of Aerospace,
Tsinghua University, Beijing, 2013. URL http://www.sciencedirect.com/science/
article/pii/S1000936113001581.
James Barrowman. Calculating the center of pressure of a model rocket. Techni-
cal report, Centuri Engineering Company, 1988. URL http://ftp.demec.ufpr.br/
foguete/bibliografia/tir-33_CP.pdf.
Maarten Uijt de Haag. Basic aerodymamic principles and applications. Techni-
cal report, Ohio University, n,d. URL http://www.ohio.edu/people/uijtdeha/
chapter-2---basic-aerodynam.pdf.
Neha Ravi Dixit. Evaluation of vehicle understeer gradient definitions. Master’s thesis,
The Ohio State University, 2009.
Glenn Research Center. Incorrect theory #1, 2014. URL http://www.grc.nasa.gov/
WWW/k-12/airplane/wrong1.html. Editor: Tom Benson.
Jr. John D. Anderson. Introduction to Flight. McGraw-Hill Book Company, fifth edition,
2005.
Joseph Katz. Aerodynamics of race cars. Annual Review of Fluid Mechanics, 38(1):27–
63, 2006. doi: 10.1146/annurev.fluid.38.050304.092016. URL http://dx.doi.org/
10.1146/annurev.fluid.38.050304.092016.
Aidan Lalor. Vehicle handling characteristics and development of a formula student car.
Technical report, Swansea Metropolitan University, 2012.
Jorge Segers. Analysis Techniques for Racecar Data Acquisition. SAE International.,
2014.
Tim Tudor. An introduction to aerodymamics. Lecture, 2015.
40
41. David H. Wood. Deriving the kutta-joukowsky equation and some of its generaliza-
tions using momentum balances. Technical report, Department of Mechanical and
Manufacturing Engineering, Schulich School of Engineering, University of Calgary,
2011.
41
42. A. Further research on aerodynamic
principles
A.1. Kutta Joukowski theorem
The Kutta Joukowski theorem relates the circulation of air to the lift achieved by said air
circulation and can be seen in it’s analytical representation in Equation A.1.1, [de Haag,
n,d].
L = −SV∞Γ (A.1.1)
The theorem assumes that the flow velocity acts upon an airfoil horizontally, that the
density is constant and that a clockwise vortex has a negative sign, [Bai and Wu, 2013].
At this point, drag is equal to zero.
A.2. Boundary layer and flow separation (skin friction)
A.2.1. Boundary layer
The boundary layer is a name for the retarded flow of air near the surface of an object
due to friction between the gas and the surface of said object. This boundary layer can be
seen in Figure A.2.1 where a represents the surface of the object at which point velocity
is said to be zero and b is the outer edge where velocity is equal to the free flowing air
flowing round the airfoil. The boundary layer thickness is denoted by δ and grows as
the flow of air progresses over the distance of the airfoil. Shear stress is experienced at
the surface of the airfoil due to the friction between the air and the airfoil surface and
is denoted by τω. This shear stress contributes to aerodynamic drag in the form of skin
friction drag. The flow of air in the boundary layer is not uniform and is dependent
on the Reynold’s number, smoothness of flow approaching the surface, the shape of the
airfoil, the smoothness of the airfoil and the pressure gradient of the flow. The main
42
43. Figure A.2.1.: Boundary layer of an airfoil that has been exagerrated for demonstration
purposes, [John D. Anderson, 2005]
factor is the Reynold’s number, which defines the degree of turbulence of the air flowing
past an object. For a low Reynold’s number, the air flow in the boundary layer is known
to be laminar where air particles flow parallel to the surface. As the Reynold’s number
increases the air flow enters a transition phase and eventually becomes turbulent. The
change from laminar flow to turbulent flow is seen in Figure A.2.2. The velocity of the
air increases rapidly from zero when the air experiences laminar flow and appears to
follow the square law whereas the increase in velocity in turbulent flow is slow initially
and then increases rapidly in a linear fashion.
Figure A.2.2.: Diagram showing the laminar and turbulent boundary layers, [de Haag,
n,d]
A.2.2. Flow separation
As air flows over an airfoil it must speed up, this means that the pressure above the wing
must decrease. As the air flows further over the wing the pressure begins to increase
till it reaches a point where the pressure is greater than the free stream pressure at
43
44. the airfoil trailing edge. Once this pressure is reached the pressure becomes an adverse
pressure gradient. These changes in pressure can be seen in Figure A.2.3. The initial
high pressure seen is known as stagnation pressure where the frontal area of the airfoil
is hitting air molecules, [John D. Anderson, 2005]. Increasing the angle of attack will
Figure A.2.3.: Graph depicting the change of pressure over an airfoil with an angle of
attack of 0°, [John D. Anderson, 2005]
change the steepness of the adverse pressure gradient. If the adverse pressure gradient
is increased, a greater demand of energy is required from the molecules of air in the
boundary layer to reach the trailing edge. If the molecules do not have enough energy
they will begin to separate from the wing and create a wake where turbulence occurs
[de Haag, n,d].
Flow separation creates two problems:
• Loss of lift, known as stalling,
• An increased pressure drag.
As previously mentioned in Section 2.2, lift occurs due to increases in pressure gradients
between the two surfaces of an airfoil. Flow separation does not affect the lower surface
pressure but increases the top surface pressure. Once the top surface pressure reaches
the same pressure as below the wing there is no longer a pressure gradient and wing
stalling will occur; this is experienced at extreme angles of attack.
44
45. B. Simultaneous equations for drag
calculation
Equations B.0.1 and B.0.2 are used as simultaneous equations to find CD and RR.
F1 =
1
2
ρCDAv2
1 + RR (B.0.1)
F2 =
1
2
ρCDAv2
2 + RR (B.0.2)
Equation B.0.1 is rearranged to solve for RR and can be seen in Equation B.0.3.
RR = F1 −
1
2
ρCDAv2
1 (B.0.3)
Equation B.0.3 is then substituted into Equation B.0.2 to make Equation B.0.4.
F2 =
1
2
ρCDAv2
2 + F1 −
1
2
ρCDAv2
1 (B.0.4)
Equation B.0.4 is factorised to make Equation B.0.5.
F2 − F1 =
1
2
ρACD(v2
2 − v2
1) (B.0.5)
Equation B.0.5 is rearranged to solve for CD and can be seen in Equation B.0.6.
CD =
2(F2 − F1)
ρA(v2
2 − v2
1)
(B.0.6)
Equation B.0.6 is substitued into Equation B.0.3 to make Equation B.0.7.
RR = F1 −
1
2
ρ
2(F2 − F1)
ρA(v2
2 − v2
1)
Av2
1 (B.0.7)
Equation B.0.7 is simplified to make Equation B.0.8.
45
