43rd AIAA Aerospace Sciences Meeting and Exhibit AIAA 2005-139

10 - 13 January 2005, Reno, Nevada

Race Car Front Wing Design

John E. Shew* and Leah R. Wyman*

Purdue University, West Lafayette, Indiana, 47906

Nomenclature
Cl = 2-dimensional lift coefficient
Cd = 2-dimensional drag coefficient
Cp = 2-dimensional pressure coefficient
CL = 3-dimensional lift coefficient
CD = 3-dimensional drag coefficient
L/D = lift-to-drag ratio
X = drag force
Y = lift force

I. Abstract

T HIS work details the design and computational analysis of a race car front wing. Using XFOIL, an airfoil was
designed, based on the Selig 1223 airfoil, to produce high values of negative lift with a low corresponding drag
at a fixed angle of attack. The modified airfoil achieved an 8.55% increase in lift and 45.6% decrease in drag over
the Selig airfoil. The airfoil design was extruded into a 3-dimensional wing, which was then computationally
analyzed using FLUENT under three different sets of conditions: wing out of ground effect, wing in ground effect,
and wing with endplates in ground effect. The results of the computational analysis are presented in the form of
pressure distribution, lift and drag coefficients, lift curves, drag polars, lift force, and drag force, as well as flow
visualization output by FLUENT. The FLUENT case for the wing with endplates in ground effect achieved an 81%
increase in lift while increasing its L/D from 6.9 to 9.0 from the case of the wing out of ground effect and without
endplates. The results conclusively show that the completed design successfully accomplishes the goal of achieving
appropriately high lift with corresponding low drag at a small angle of attack.

II. Introduction
The front wing of a race car is a necessary component to make cornering at high speeds safer. There are other
means to achieve the downforce necessary for high-speed cornering, but many of them have been prohibited due to
instability and unpredictability, leaving wings as the primary means of creating downforce for many race cars. An
inverted high-lift wing creates a large amount of negative lift, which increases traction for the car, making the
chance of spinning the car significantly less. Banking and cornering power may be increased proportionately to the
downforce available. Drag should be taken into consideration because, especially during the straight-aways of the
race, the drag force reduces the acceleration and the top speed of the vehicle. Conservation of fuel is also a benefit of
low drag. The design space was based on a Formula 1 race car using data obtained on the internet and in the 2003
Formula 1 Technical Regulations. The goals of this design were to achieve high lift with corresponding low drag at
a small angle of attack within the design space.
The final 2-dimensioncal design consisting of a modified airfoil shows significant increases in the lift coefficient
from the original airfoil as well as a large decrease in the drag coefficient, showing gain for our 2-dimensional
design without suffering losses. The final 3-dimensional design consists of a modified airfoil used to create a wing
with endplates. End-plates were added in order to keep the performance of the wing closer to that of a 2-
dimensional airfoil by reducing 3-dimensional effects. The Pro/Engineer model of the designed wing with endplates
can be seen in Figure 1.

*
Undergraduate Student, School of Aeronautics and Astronautics, 1282 Grissom Hall, West Lafayette, IN 47906,
Student Member.

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Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
 Figure 1: Pro/Engineer model of the designed wing

The history of open-wheel race cars was studied insofar as what characteristics are vital to the wing design as
well as what rules are currently in place pertaining to the front wing of race cars. The aerodynamics of race cars
basically adheres to two objectives: to increase the speed by reducing the drag, and to increase aerodynamic
downforces in order to improve traction, banking, and cornering power (p. 138, Geoffrey Howard)1. While the latter
has been creatively explored, the reduction of drag has mainly been accomplished only by decreasing the frontal
area. Other methods of drag reduction should be explored. One major limiting factor on this reduction is the
downforce needed. There has to be a balance between the two objectives of increasing top speed and being capable
of efficiently and safely varying from a straight path. The purpose of the airfoils on the front and back of a race car
is to provide negative lift. The cost for this increased downforce is increased drag. The major limiting factors on
these airfoils are the imposed technical and safety guidelines. A minor limiting effect is the weight, minor since the
front airfoil is being studied and weight in the front is preferred (Howard).

III. 2-Dimensional Airfoil

The 2-dimensional design was the first part of the actual design to be undertaken after determining the design
space and studying the background. For the purpose of a front wing on a race car, the airfoil has a fixed angle of
attack, and that must be taken into account for the design. The most important consideration was the overall design
goal of achieving high downforce with small drag. The lift and drag coefficients must be evaluated in the 2-
dimensional design to assure the accomplishment of this goal.

A. Original Airfoil Selection

Using the UIUC Airfoil Coordinates Database2, 41 airfoils were chosen based on their categorization as high lift
or their physical resemblance to known high-lift airfoils. The coordinates for these airfoils were saved in a file
format compatible with XFOIL. The airfoils then underwent an elimination process by comparing the performances
against one another. The lift curves and drag polars were compared appropriately within the design space until one
airfoil, the Selig 1223, was proven to have the best performance for the design criteria. The specifics of the qualities
desired included a drag polar with a high lift coefficient at low drag values. The drag polar farthest left on a graph of
Cl vs. Cd shows this, although it is important only for the chosen range of Cl (1.3-2), not necessarily the entire drag
polar. The drag bucket, the area on the drag polar with lowest drag, needs to encompass the desired values of Cl
(1.3-2). The lift curve is another feature used to choose one airfoil over the others. It is desirable to keep the angle
of attack low in order to keep profile drag low, so the lift curve which is shifted farthest left is best since this
signifies higher lift at lower angles of attack.

B. Computational Setup
XFOIL was the program used to modify and evaluate the pre-existing Selig 1223 airfoil. A Reynolds number of
2,000,000 and a Mach number of 0.23 were input as the running conditions, which correspond to an average race car
speed which is about 80 m/s (179 mph). For the plot of the pressure coefficient versus the chord, a flat pressure
distribution (rooftop) and a Stratford recovery were desired for a small range of low angles of attack, which would
help achieve increases in the lift coefficient and decreases in the drag coefficient. XFOIL was used to iteratively
modify the pressure distribution of the airfoil until an airfoil seven generations removed from the original Selig 1223
was chosen as the final 2-dimensional design. The final pressure distribution for the modified airfoil compared to
the original pressure distribution for the Selig 1223 airfoil can be seen in Figure 2a and Figure 2b.

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Figure 2a and 2b: The pressure distribution comparison of the Selig 1223 airfoil and the modified airfoil at 5°
angle of attack (Re = 2e6, M = 0.23)

C. Results and Discussion

The main aerodynamic qualities of interest for the 2-dimensional design are the lift coefficient and the drag
coefficient for varying angles of attack. The range for the lift coefficient in the problem space was used to choose
the range of optimum angles of attack, from which the best value could be chosen. Table 1 summarizes the lift and
drag coefficient values, comparing the original Selig 1223 airfoil performance to the modified airfoil performance.
The table illustrates why the 5º angle of attack is appropriate: at that value the percent decrease in the drag is
significantly larger than the preceding decrease and the next increase of angle of attack shows an actual increase in
drag rather than a decrease, and the lift coefficient percent increase is only slightly lower than those for the
preceding and consecutive angles of attack.

Table 1: Lift and drag coefficients for varying angles of attack for the Selig 1223 and the modified airfoil and
the relationship between them

Original Selig
1223 Modified Airfoil % increase % decrease
aoa Cl Cd Cl Cd Cl Cd
0 1.26 0.0169 1.42 0.0092 12.9 83.3
2.5 1.56 0.0115 1.71 0.0087 9.86 32.2
5 1.84 0.0132 1.99 0.0090 8.55 45.6
7.5 1.97 0.0139 2.18 0.0159 10.9 -12.7
More evidence of the improvement from the original Selig airfoil to the modified airfoil can be seen in the following
graphs with a lift curve comparison (Figure 3) and a drag polar comparison (Figure 4). The lift curve comparison
(Figure 3) illustrates a higher lift coefficient for the modified airfoil at the same angles of attack, which is favorable.
The drag polar comparison (Figure 4) shows that there is a drag bucket for the modified airfoil encompassing the lift
coefficient range of the design space, which is not seen in the drag polar of the Selig airfoil. This trend proves the
superiority of the modified airfoil for high lift and low drag design considerations within the design criteria.

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NOTE: There are fewer data points for the Selig airfoil because XFOIL would fail to converge at the higher and
lower angles of attack than those shown.
Cl vs. Angle of Attack

2.4

2.2

1.8

1.6
Cl

1.4
Modified Airfoil
Selig 1223
1.2

0.8
-4 -2 0 2 4 6 8 10 12
Angle of Attack [deg]

Figure 3: The lift curves of the modified airfoil (left) and the original Selig (right)

Cl vs. Cd

2.4

2.2

1.8

1.6
Cl

Modified Airfoil
Selig 1223
1.4

1.2

0.8
0.005 0.01 0.015 0.02 0.025 0.03
Cd

Figure 4: The drag polars for the modified airfoil (left) and the original Selig (right)

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 IV. 3-Dimensional Wing
The 3-dimensional design of the airfoil consisted of three main steps. The first step was to model and analyze a
3-dimensional wing based on the designed 2-dimensional airfoil. The second step was to model and analyze the 3-
dimensional wing in ground effect. The third step was to model the 3-dimensional wing in ground effect with
endplates added. FLUENT cases were run for each step to allow comparison of the differences in performance that
each step makes.

A. Computational Setup
The 3-dimensional wing was modeled in Pro/Engineer. Coordinate points for the 2-dimensional airfoil were read
into Pro/E as datum points and used to create half of the 3-dimensional wing. Only half of the wing was modeled in
order to reduce the amount of time needed for FLUENT cases to run. (Utilizing a plane of symmetry in FLUENT
makes this shortcut possible.) The planform is rectangular with a chord, c = 0.3m, and span, b = 1.4m based on
the dimensional constraints for Formula 1 race cars. The angle of attack was set to 5°, corresponding to the best
angle of attack for the 2-d airfoil. These dimensions for the wing with endplates can be seen in Figure 5.

Figure 5: Three-view of wing with dimensions

The Pro/E model was saved in step format and input into Gambit 2.0.4, which was used to create a mesh of the
wing geometry. A box was created around the wing to create the domain of the airflow, and then the tri pave
meshing option was used to create a fine mesh along the surface of the wing. This was followed by the
implementation of tet/hybrid meshing to mesh the volume inside the box. The volume was set with a velocity inlet
boundary condition in front of the wing and a pressure outlet boundary condition behind the wing. As previously
noted, a symmetry boundary condition is applied on the side of the wing perpendicular and connected to the span in
order to model the half wing as if it were part of a full wing. Wall boundary conditions were set for the faces of the
box volume above, below and to the side of the wing. The mesh was then exported for use in FLUENT.
The exported mesh of the wing was read into FLUENT 6.0. The grid was checked and then scaled to set the
dimensions of the wing modeled in FLUENT equal to the dimensions of the design. A two equation, k-ε turbulence
model was used for modeling turbulence within the flow. A velocity input of 80 m/s (179 mph) was used to model
the airflow seen by a Formula 1 front wing at average race speeds. The boundary condition for the wall below the
wing was set as a moving wall with velocity of 80 m/s (179 mph) for the models analyzing ground effect, in order to
match the velocity input and more closely represent a car driving on a track.

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B. Results and Discussion
The first case run in FLUENT was for the 3-dimensional rectangular wing without endplates and out of ground
effect. The main reason for running this case was to allow the examination of the performance of a wing based on
the designed airfoil. Another important reason for running this case was to give a bench mark for analyzing the
improvement that adding endplates and putting the wing in ground effect would have on the performance of the
wing. The drag force and the lift force are the most important data values returned by FLUENT when considering
the wing performance in relation to the race car. The lift force exerted by the wing out of ground effect and without
endplates was calculated by FLUENT to be -1971 N and the drag force was calculated to be 286 N. The lift force is
negative because the wing is inverted, so the force is downwards. Since only half of the wing was modeled in
FLUENT, all the forces have been multiplied by 2 to give values for the full wing. This is within the middle of the
range of the design space that was established for this project.
The second case run in FLUENT was that of the wing without endplates but in ground effect. The expected
results should show an increase in lift due to the Venturi effect created by the proximity of the wing to the ground.
This is exactly what was observed in the data returned from FLUENT, with the lift force calculated to be -2901 N.
The lift force of the wing in ground effect was 47% greater than the lift for the wing not in ground effect. The drag
force increased as well and was calculated to be 418 N. The pressure difference caused by the ground effect can be
seen in Figure 6 and Figure 7 which show the pressure contours for the wing out of and in ground effect,
respectively. A much larger area of lower pressure is seen below the wing in ground effect as compared to the wing
out of ground effect. The pressure color scale for Figure 6 is -6.94e3 Pa to 4.87e3 Pa and for Figure 7 it is -1.03e4
Pa to 4.35e3 Pa.

Figure 6: Wing out of ground effect Figure 7: Wing in ground effect

The third and final case run in FLUENT was that of the wing in ground effect and with endplates. The
justification for adding endplates to the inverted wing is to impede the flow of air around the tips of the wing, which
helps to increase lift by decreasing upwash. This flow around the tip of the wing can be seen in Figure 8 which is a
pressure contour and velocity vector plot for the tip of the wing out of ground effect and without endplates. Adding
endplates to the wing impedes this flow, allowing the wing to be more efficient and thereby produce more lift. The
lift force calculated for the wing was -3567 N, which is an increase of 23% from the lift produced by the wing in
case 2 and 81% from the lift produced by the wing in case 1. The drag force calculated for the wing in ground effect
with endplates was 397 N, which is a 5% decrease in drag from the wing in case 2. Table 2 displays the lift and drag
forces and the lift to drag ratio for the three cases. The lift-to-drag ratio allows a comparison of how efficiently the
wing operates. Bringing the wing into ground effect increases the lift and the drag at the same proportion, therefore
the L/D ratio of cases 1 and 2 are identical. Adding endplates does not increase the lift as much as the ground effect
does, but drag is decreased slightly. Therefore, the L/D ratio for case 3 is higher than that for cases 1 and 2, which
demonstrates the improvement in efficiency achieved by the addition of endplates. The figures that follow allowed
for visual analysis of the flow over the final design of the wing, in ground effect and with endplates. Figure 9 shows
the interaction of pressure between the wing and ground via displayed static pressure contours on the ground and
across the span of the wing at about ½ chord of the wing. This interaction shows that the wing is still affected by 3-
dimensional flow; that is, the low pressure seen at the middle of the span of the wing does not extend out to the tip
of the wing. Figure 10 and Figure 11 show the filled static pressure contours along the top and bottom surface of the

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wing, respectively. Typical pressure contours of an inverted wing show a spike of pressure at the leading edge, a
slightly higher than free stream pressure on the top of the wing, and an area of lowest pressure on the bottom of the
wing immediately after the leading edge. The area of low pressure for this wing design extends farther along the
chord than most wings due to the larger area of flat pressure distribution achieved by the modified 2-dimensional
airfoil. The lower pressure area seen on the endplate in the bottom view of the wing is where the flow curls around
the far side of the endplate to the underside of the wing, which is discussed and shown in more detail below and in
the following figures. Figures 12 - 15 display the path lines of particles released into the flow from the wing surface.
This visualization is useful in studying how the air flows over the wing and around the endplate. The coloring of the
lines is based on the particle numbering system and has no relevance to the visualization except to make the flow
easier to distinguish. Figure 12 shows the expected upturn of the flow and roll-up of the wake behind the wing.
Figure 13 shows a closer view of the wing giving a better view of the flow at the endplate. Figure 14 and Figure 15
show the top, outside of the wing and endplate, and bottom, inside of the wing and endplate, respectively. These
figures show that although the flow around the tip of the wing is impeded by the endplate, it is not eliminated. The
flow can be seen flowing up over the top of the endplate, down and across the outside and underneath and around
the bottom of the endplate.

Table 2: Force values for FLUENT cases

Full Wing Values

X [N] Y[N] Y/X
(Half Wing Values
(drag force) (lift force) (lift/drag)
multiplied by 2)
Case 1:
No ground effect 286 -1971 6.9
No endplate
Case 2:
Ground effect 418 -2901 6.9
No endplate
Case 3:
Ground effect 397 -3567 9.0
Endplate

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Figure 8: Pressure contours and velocity vectors at tip of wing

Figure 9: Pressure contour at ½ chord and along ground

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 Figure 10: Pressure contours on top of wing

Figure 11: Pressure contours on bottom of wing

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 Figure 12: Particle pathlines of wing wake

Figure 13: Particle pathlines around endplate

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Figure 14: Particle pathlines around bottom, inside of endplate

Figure 15: Particle pathlines around top, outside of endplate

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 V. Conclusion
The completed design successfully accomplishes the original goal of achieving appropriately high lift with
corresponding low drag at a small angle of attack, 5º. These results were achieved by improving the 2-dimensional
airfoil, adding endplates, and taking advantage of ground effects, all while staying within the constraints set by the
2003 Formula 1 Technical Regulations and other design considerations. The final lift values exceeded those in the
original requirement range, as can be seen in Table 3.

Table 3: Summary of final values and initial goals

X [N] Y[N]
(drag force) (lift force)

Final Design 397 -3567

Initial Design
- -1470 to -2350
Goal
The implication of this increased negative lift force while maintaining a reasonable drag force is increased safety
to take turns at higher speeds without too much of a penalty in top speed and acceleration for a race car which
utilizes this wing in the specified conditions. Safely traveling at higher speeds with little impedance to performance
on straight-aways increases the probability of winning races, the primary purpose of any race car.

VI. Acknowledgements
The authors would like to thank the following Purdue University faculty, students, and alumni for their guidance
and support of this project: Prof. John Sullivan, David Loffing, Leon Walters, James Gregory, and Christopher
Peters. Also, this project would not have been possible without the original Selig 1223 airfoil coordinates designed
by Prof. Michael Selig, University of Illinois at Urbana-Champaign.

References
1
Howard, G., Automobile Aerodynamics, Osprey Publishing Ltd., London, 1986.
2
UIUC Airfoil Coordinates Database, http://www.aae.uiuc.edu/m-selig/ads/coord_database.html, 2002.
3
Drela, M., http://raphael.mit.edu/xfoil/.

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