This document discusses how aerodynamics can improve vehicle performance in various racing events by increasing downforce. Downforce pushes the tires into the road, allowing for increased cornering ability without a significant weight penalty. Analysis of the skid pad, slalom, and acceleration events shows that a car with an aerodynamic package could achieve faster lap times by producing higher lateral and transient lateral forces. While drag also increases with downforce, the calculations show the engine power is sufficient to overcome these forces for the speeds in these events. Therefore, an aerodynamic package has the potential to significantly improve performance.

1. 1
Aerodynamics
TABLE OF CONTENTS:
 Do we need aerodynamics?-----------------------------------------1
o Vehicle Dynamics Analysis---------------------------------1
o Slalom-----------------------------------------------------------7
o Acceleration event------------------------------------------10
o Braking---------------------------------------------------------11
o Autocross/Endurance--------------------------------------12
o Summary------------------------------------------------------20
 Design requirements-------------------------------------------------20
 Flow over the front tires---------------------------------------------20
 Rear wing optimization-----------------------------------------------22


2. 2
Do we need aerodynamics?
Vehicle Dynamics Analysis
In a race car, driving, braking and cornering forces are created at the contact patch between the tire
and the road. These friction forces are strongly affected by the vertical forces applied on the tires and are
limited by a friction coefficient, this means that a car can turn up to a given maximum speed, but once it
exceeds this speed, the car will slide, this is a result of exceeding the limit of the tire adhesion coefficient.
Based on this idea, if we could increase the normal tire force by pushing the tire more against the road, then
the cornering force could be increased too, without the risk of sliding. Aerodynamic downforce increases
the load on the tires by increasing the vehicle's weight very little, the result is increased cornering ability
with little weight penalty, which gives a reduction in lap times.
The lateral balance of a car can be illustrated by a simple expression (assuming steady-state cornering):
μ(mg + Dz) =
mV2
ρ
(Eq.1)
where:
 μ: coefficient of adhesion of the tires
 g: gravity (9.81m/s2)
 Dz: downforce
 m: mass of the car (215.5kg)
 V: velocity
 ρ: radius of curvature
The left hand side of eq.1 represents the lateral force that the car can sustain before sliding. Dividing both
terms by the mass, the equation can be rewritten as;
G′
s =
Vmax
2
ρ
(Eq.2)
where:
 G's: Lateral "g's" at which the tires will slip in steady state cornering (mg+Dz).
Rearranging eq.2:
Vmax = √G′s ∙ ρ (Eq.3)

3. 3
This equation is particularly important, since it describes the lateral dynamic of the car in Skid Pad.
The time required to complete a lap at the Skid Pad contest is given by;
tSP =
2πρSP
Vmax
(Eq. 4)
where:
 tSP: time to complete a lap at the Skid Pad contest
 ρSP: radius of curvature at the Skid Pad contest (9.125m)
Combining equations 3 & 4:
tSP = 2π√
ρSP
G′s
= f(G′
s) (Eq.5)
therefore the lap times and speed at the Skid Pad event can be calculated in terms of the G's;
Based on the vehicle requirements specified in section 1.7 (Steady state lateral acceleration of 1.48
G's), the expected time is 4.96 seconds and the velocity achieved will be 25.8mph. It is important to note
that in the Skid Pad event the first cars can be measured in less than tenths of a second, therefore the ability
to produce the required downforce is critical. This table shows the Skid Pad times at Lincoln 2012.

4. 4
The next step is to
calculate the downforce the car must create to produce the required lateral
G's.. From Eq. 1 and solving for Dz:
G′
s =
μ(W+Dz)
m
Dz =
G′s∙m
μ
− W
Everything on this equation is known, except for μ. The value of μ is unknown because the tire behavior
depends on multiple factors, such as temperature, pressure, vertical load, etc. However, based on the data
sheet published by Hoosier (tire provider), values between 1.3 and 1.7 can be expected. Plotting the required
downforce in terms of the coefficient of adhesion of the tires:
Skid Pad times, Lincoln 2012
Downforce required vs. tire adhesion coefficient

5. 5
It is important to note that if μ is larger than 1.5 it is not required to produce downforce in order to
achieve 1.48 G's. If that is the case, that downforce can be "invested" into cornering at a higher lateral
acceleration.
Before continuing, it must be demonstrated that drag and rolling resistance produced in this even
will not prevent the car from achieving the maximum velocity calculated from the lateral balance. As such,
the longitudinal balance must be analyzed. The forces acting on the car in the longitudinal direction can be
illustrated as:
 Model 1 : R = (0.005 +
1
P
(0.01 + 0.0095 ∙ (
v
100
)
2
)) ∙ (W + Dz) (Eq.7)
 Model 2: R = (0.01 + 6.5 ∙ 10−6
∙ v2) ∙ (W + Dz) (Eq.8)
 Model 3: R = Pα
∙ (W + Dz)β
∙ (a + bv + cv2) (Eq.9)
where:
 R:Rolling Resistance
 P:Tire pressure
 v:velocity
 α,ß,a,b,c: SAE J2452 coefficients
 Dz: Downforce =
1
2
ρv2
AfrontalCd (Eq.10)
 Dx: Drag =
1
2
ρv2
AfrontalCx (Eq.11)
Note that models 1 and 3 are pressure and velocity dependent, whereas model two is only velocity
dependent.
Based on previous cars and the track conditions:
 P≈10.5 psi
 Afrontal≈1.4m2
 Cd≈2.5
 Cx≈1.3
Longitudinal forces acting on a car

6. 6
 α= -0.003, ß= 0.97, a= 84·10-4, b=6.2·10-4s/m, c= 1.6·10-4s2/m2
Comparing the drag produced by an average FSAE car with a full aerodynamic package with the
rolling resistance:
The figure above shows that the three models are very similar, even though model three predicts a larger
rolling resistance at higher speeds. Comparing the rolling resistance to the drag (see next figure).
It can be concluded that the rolling resistance plays an important role at low speeds (0-20mph). Once
the car exceeds that speed, the contribution of the rolling resistance stabilizes (20-25% of the overall
contribution). Therefore for the Skid Pad event, where the velocities are in the range of 0-30mph, in order
to get more accurate results, it will be assumed that the rolling resistance adds an additional 25% non-
aerodynamic drag. Adding the rolling resistance (average of the three models) and the aerodynamic drag,
the power required to overcome drag and rolling resistance is:
Rolling Resistance and Drag comparison vs Speed
Relative Importance of the Rolling Resistance

7. 7
The figure above shows that for the range of speeds present in the Skid Pad event, the engine is
capableof overcoming the power absorbed by the aerodynamic system and the tires. Based on longitudinal
and lateral balance, the limiting factors are the tires (limited adhesion coefficient) and not the drag!
In light of the previous analysis, an addition of an aerodynamic package will not harm the times obtained
at Skid Pad. In fact, the analysis suggests a car with an aerodynamic package would receive better times, as
would allow greater lateral G's and, therefore, greater velocity. However, this analysis is slightly optimistic,
given:
 The slight reduction of aerodynamic downforce measured at high yaw angles.
 The effect of the suspension system.
More complex calculations will show that Skid Pad performance with and without wings is nearly
equal, a fact corroborated by Skid Pad tests with LMS11 and LMS12 with and without aerodynamic
packages.
Slalom
Another path where the influence of the downforce can be analyzed is the Slalom. Assuming the
cones are in a straight line and equally spaced, the car follows a sinusoidal path through cones, the amplitude
of sine wave is half outside track of tires (to), plus half the pylon base (c), and the clearance between the
tire and the cone (d):
Power absorbed by the Rolling Resistance and the Drag

8. 8
The
spatial sine wave is given by: y = Asin(wxx) (Eq.12)
where A =
(to+c)
2
+ d (Eq.13) , wx is the spatial frequency of the slalom wx =
π
L
(Eq.14),
also the distance traveled, x is given approximately by x= vt (Eq.15)
yielding to: y = Asin(
πvt
L
) , the acceleration in the lateral direction, y, is then ÿ:
ÿ = −A(
πv
L
)2
sin (
πvt
L
) (Eq. 16)
and the maximum acceleration in G's is:
maxG′
s =
A
g
(
πv
L
)2
(Eq.17)
the period (T=L/v) between cones as a function of the slalom amplitude at various G's:
From
figure 16, it can be concluded that by maximizing the maximum transient lateral acceleration, the time
required to drive through the slalom can be significantly reduced. Assuming a five cones slalom (amplitude
of 50 in), the difference of time between a car without an aerodynamic package (max transient lateral force
Slalom
Time between cones at various G's

9. 9
of approximately 1 G's) and a car with an aerodynamic package (max transient lateral acceleration of 2 G's)
can be calculated from the Table 2.
Time between cones at various G's
Time difference = 5 ∙ (1.13 − 0.8) = 1.65 seconds‼!
The difference in performance through a slalom between a race car with and without an aerodynamic
package is remarkable, particularly in the Autocross and Endurance events, where there are multiple
slaloms, and the difference in time between the top ten teams might be less than a tenth of a second, as seen
in the table below. Note that for the 2013 the Endurance track includes four slaloms, a fact that could make
a car with an aerodynamic package up to six seconds faster than one without. Therefore it can be concluded
that an aerodynamic package significantly improves the car's performance through a slalom. Note
that the addition of wings to the aerodynamic package is both beneficial and detrimental in this situation.
At low speeds, the increased polar moment of inertia due to the addition of wings will result in lower yaw
accelerations compared to a car without wings. But above a critical speed, the increased grid due to the
downforce will result in higher potential yaw acceleration rates for the winged car.
Autocross times. Lincoln 2012

10. 10
Acceleration
The next event to analyze in determining the worth of an aerodynamic package is the Acceleration
event. The maximum performance in longitudinal acceleration is determined by three limiting factors:
 Drive tires' traction
 Engine power
 Top speed is limited by drag and tire rolling resistance
At top speeds the limiting factor may be traction limited and at high speeds it may be power limited.
From the free body diagram (Figure 11), applying ∑ Fx = 0:
m ∙ ax = Ft − Dx − R (Eq.18)
where:
 Ft: Tractive force
 R: Rolling Resistance
 Dx: Drag
 ax: Longitudinal acceleration
Multiplying eq. 18 by the velocity of the car, substituting R (model 2 will be used, because of its
simplicity, but still accurate results) Dx and rearranging terms:
where:
 Peng: Engine's power (65 bhp restricted)
 Afrontal: Frontal area of the car (1.4m2)
 Cx: Drag coefficient based on the frontal area
 Cz: Downforce coefficient based on the frontal area
From equation 19 it is easy to conclude that the drag and downforce (which influences the rolling
resistance) generated by the aerodynamic package will lead to slower acceleration times. Note that even
this simple model, where the longitudinal weight transfer is not included, predicts that a car with an

11. 11
aerodynamic package will produce slower times at the acceleration event than a car without it. Based
on Scott Wordley and Jeff Saunders' paper "Aerodynamics for Formula SAE: Initial design and
performance prediction" a winged car should be able to accelerate slightly faster than the same car without
wings at velocities below 30 mph due to the increase in aerodynamic downforce. This is an interesting
observation, particularly considering that the corner exit speeds for events like Autocross and Endurance
are typically in the 20 to 40 mph range.
Braking
Another circumstance where a car with an aerodynamic package will improve better than the one
without it, is Braking. The free body diagram of a vehicle braking is:
Summing the force in the x direction: ∑ Fx = 0
−max − Fbf − Fbr − Dx = 0 (Eq.20)
where:
 ax: longitudinal acceleration
 Fbf:Front brake force
 Fbr: Rear brake force
 Fb:Total brake force
Front and rear braking force terms arise from the torque of the brakes on the wheels, rolling resistance,
bearing friction and driveline drag. Taking into account that Fbf + Fbr = Fb
Figure 1-Braking free body diagram

12. 12
max = −Fb − Dx (Eq.21)
ax = −
(Fb + Dx)
m
(Eq. 22)
and substituting Fb = μ(W + Dz),
−ax =
(μ(W+ Dz) + Dx)
m
=
(μ(W+
1
2
ρv2
AfrontalCd) +
1
2
ρv2
AfrontalCx)
m
(Eq.23)
−ax =
(μW +
1
2
ρv2
Afrontal(Cdμ + Cx)
m
(Eq. 24)
Assuming realistic parameters for a Formula SAE car with and without an aerodynamic package:
The deceleration
achieved by the car with an aerodynamic package is always larger than the one produce by a car without an
aerodynamic package, particularly since the car with an aerodynamic package produces more drag, which
is beneficial when braking, and because the downforce produced enhances the grip of the car and hence the
mechanical braking capabilities. Hence it has been demonstrated that a car with an aerodynamic package
improves the braking capabilities of a Formula SAE car, which means that the driver can brake later
and based on the previous conclusions he will be capable to corner at a higher speeds,all of this thanks
to the aerodynamic package.
Autocross/ Endurance
A comprehensive lap-time simulation of the Autocross/Endurance track(s) is required for a
thorough analysis of the effect of adding an aerodynamic package to a Formula SAE car. Two different
programs were used to determine the trade-offs in an aerodynamic package.
Downforce and drag coefficient for Formula SAE cars

13. 13
LapSim, the first program used, utilizes a majority of vehicle parameters to simulate a vehicle
running a track. The code includes weight transfer. Simulation results deviated as little as 5% from real-
world competition values. The parameters used in order to simulate the lap times are:
 Tires: Hoosier 13''
 Vehicle weight (including driver):
 With a full aerodynamic package: 575lbf
 With a small aerodynamic package (nose, sidepods and undertray):470-570 lbf
 Without aerodynamic package (only nose and sidepods): Variable, 450-570 lbf
 Wheel base: 60 in
 Track width: 54 in
 Center of Gravity: 11.5 in off the ground
 Final drive ratio: 5.5
 Downforce at 40mph
 With a full aerodynamic package: Variable,100-260 lbf
 With a small aerodynamic package: 50 lbf
 Without aerodynamic package: 5 lbf
 Aerodynamic Efficiency:
 With a full aerodynamic package: 2.4
 With a small aerodynamic package: 2.8
 Without aerodynamic package: 0.1
 The track where the simulations are done, is the 2011 Endurance FSAE West Competition Circuit
(USA).The Circuit is shown in Figure 19.
Comparing a car without an aerodynamic package whose requirement is to reduce weight (variable between
450 and 550 lbf) and two cars with an aerodynamic package (the full aerodynamic package with variable
downforce generated at 40 mph, from 100 to 250lbf, and the one with a small aerodynamic package trying
to cut weight) the times for Autocross, Skid Pad and Acceleration are shown.

14. 14
Figure 20 clearly shows that the car with a full aerodynamic package will always beat a car with a
small or no aerodynamic package at the autocross event, this is because the event features many slaloms,
corners and few straights. A set-up with large downforce values results in faster slaloms and turns. There
is, however, a small region where the car with a small aerodynamic package could beat the car with a full
package. This is not an interest region for LoboMotorsports, as it requires a car that weighs 310 lbf, a value
well outside the projected weight of the team's car (425-525 lbf). Furthermore, it would only beat the car
with a full package only if the latter produced less than 125 lbf of downforce at 40 mph, an unlikely
occurrence. Considering a normal situation (based on previous cars), where the car with the full
aerodynamic package produces around 175 lbf of downforce at 40 mph and weights 475 lbf and the car
with small or no aerodynamic package weight around 400lbf.The difference in lap times is approximately
3 seconds for the car with a small package and 4.5 seconds for the car without an aerodynamic package.
This is relevant because Autocross and Endurance are very similar events, together gathering 450 (not
counting fuel consumption) out of 1000 points, and this simulation indicates that a full aerodynamic
package significantly reduces lap times.
Besides these analytical considerations, the cars manufactured in the LoboMotorsports race team
are not driven by professional drivers, and according to amateur drivers, a car with an aerodynamic car is a
lot easier to drive due to straight line stability and increased lateral grip. As each cone hit in Autocross and
Endurance incurs a two-second penalty, stability and grip are essential to a competing race car.
Autocross comparison between different aerodynamic packages

15. 15
Skid Pad comparison between different aerodynamic packages
The analysis of the Skid Pad event corroborates the analytical conclusion made in the Skid Pad
section. The more downforce produced by the car, the more G's it will pull; the car will drive faster and will
get better times. Note that the reduction of weight doesn't cut Skid Pad times, as mass by itself will be
cancelled out if the car produces little downforce (contribution is negligible compared to the mass term) or
none ( μmg = m
v2
ρ
). As previously stated, the suspension system is a determinant factor. Based on
experience with other cars, an optimized suspension setup might be more valuable than an aerodynamic
package on its own.
Acceleration comparison between different aerodynamic packages
Figure 22 demonstrates that aerodynamic packages increase drag and rolling resistance of the entire
system, making the car more sluggish. For the acceleration event, then, the car with the full aerodynamic

16. 16
package should have the capacity to change the angle of attack for the rear and front wings, as the amount
of downforce produced in this event doesn't improve the car's times (recall that downforce improves car
acceleration at speeds higher than 30 mph, speeds tested at the end of the track). If the aerodynamic system
has the capacity to change the wings' angle of attack, the equivalent downforce produced at 40 mph would
be around 100 lbf, meaning the car would cut between 0.6-0.8 seconds, compared to the same car at the
high downforce configuration.
The second software used to analyze the impact of an aerodynamic package is OptimumLap.
OptimumLap is software developed by OptimumG, an international vehicle dynamics consultant group that
works with automotive companies and motorsports teams to enhance their understanding of vehicle
dynamics through seminars, consulting and software development.
The vehicle model used in OptimumLap is a point mass, quasi-steady state model. Mathematically this is
overly simplistic, but in reality, this model is very powerful at analyzing the global performance trends of
a vehicle, without having to capture or model more detailed effects. The advantage of this is that a vehicle
can be characterized by very few inputs, requiring very little time to setup and conduct a simulation. Even
as the model is a point-mass model, meaning that no weight transfer or transient affects are taken into
account, the simulated results do correlate well with logged data. Validations have shown that apex speeds,
end of straight speeds, energy consumption and total lap time all match reality within 10% (often within
5%), confirming that OptimumLap is a tool well suited to study the global trends and the impact of each
vehicle subsystem.
Creating a vehicle in OptimumLap is a very straightforward process especially since it requires a small
number of inputs. The vehicle is defined by the following parameters:
Logged data compared against model results using OptimumLap

17. 17
 Mass: 575 lbf including driver
 Drag and downforce coefficient: 1.3 and 3 respectively
 Frontal area: 15.2 ft2
 Tire radius and rolling resistance coefficient: 10'' and 0.015 respectively.
 Engine data. The engine's curves for torque and power are taken from Ricardo software.
 Transmission type: CVT
 Track: FSAE Endurance Nebraska 2012 (figure 29)
FSAE Endurance Nebraska 2012,Lincoln USA
The first analysis considered in order to determine the impact of an aerodynamic package, is the
comparison of a car with an aerodynamic package (whose goal is to create downforce) and a car without an
aerodynamic package (whose goal is cut weight). In order to simulate this analysis, two parameters have
been varied simultaneously, vehicle's mass and downforce coefficient.
 Downforce coefficient: 0 - 3.5
 Vehicle mass: 350 - 500 lbf ( the driver's weight has been included in the model, 150 lbf )
The results produced by OptimumLap can be seen in Figure 30 (next page).Comparing the most
likely situations for FSAE cars the car with an aerodynamic package (downforce coefficients between 2
and 3.5, and vehicle weight around 650 lbf, blue star on figure 30) will always defeat a car without an
aerodynamic package (downforce coefficient close the zero, weight around 550 lbf, red star on figure 30),
even though the cars with an aerodynamic package weigh more. It is very interesting to realize that
producing downforce is more efficient than cutting weight in terms of lap times for autocross and endurance,
hence the development of an aerodynamic package seems to be a better solution to get better results instead
of simply cutting weight. Based on these results, the implementation of an aerodynamic package reduces
the lap times by few seconds every lap for the autocross and endurance event.

18. 18
The next aspect that must be considered is the balance between downforce and drag. As a rule of
thumb the more downforce our system produces the higher the drag, hence an analysis of the interaction
between drag and downforce must be done to conclude at what point creating too much drag and downforce
may hurt the lap times. Figure 26 exhibits the results for different drag and downforce coefficients and their
impact. Figure 26 clearly shows that a car that produces a lot of downforce (downforce coefficients of 3-
3.5) is faster than any low downforce configuration, even though their drag coefficient is higher. High
downforce configuration (blue star) and low downforce configuration (red star), clearly demonstrate this
fact.
It is very important to highlight that the circuit at Lincoln (Nebraska), competition where
LoboMotorsports compete, is considered a "High Downforce" track, hence the simulations show that having
Impact of downforce coefficient vs vehicle mass in lap times
Impact of downforce vs drag coefficients in lap times

19. 19
a massive aerodynamic package always improves the car's performance. In other competitions, the balance
between downforce and drag must be analyzed, since in faster tracks the addition of too much drag and
downforce might hurt the car's performance. An example of "Low Downforce" track is FSAE Endurance
Michigan 2012 (figure 28).
Comparing the lateral acceleration achievable by a car with a full aero package and one without it a large
aero package is necessary to achieve the lateral acceleration requirement.
Figure 27 demonstrates the better capacities of a car using an aerodynamic package while cornering,
this matter can be observed in the difference between the lateral g's peaks.
In summary, with respect to the various Dynamic Events, it has been shown theoretically, that the addition
of an aerodynamic package to the LoboMotorsports FSAE car should result in:
 Acceleration Event: Slower times. The expected loss in time is 0.4-0.8 seconds, assuming a change
in the angle of attack of the wings into a lower drag configuration.
 Skid Pad: Similar or marginally faster times. The suspension's setup is more decisive.
 Autocross and Endurance events:
Lateral acceleration comparison
FSAE Endurance Michigan 2012 USA

20. 20
o Slower straight-line acceleration
o Significantly higher cornering speeds
o Significantly higher slalom speeds
o Slower yaw acceleration at low speeds, higher yaw acceleration at high speeds.
o Faster times, in the order of seconds.
o Increased fuel usage
All the reasons previously stated, have made LoboMotorsports decide to implement an
aerodynamic package in order to improve the car's performance.
Design Requirements:
 Full aerodynamic package with 2 element front wing, rear wing ,and undertray
 Car Downforce: 146 lbf at 40 mph
 Car Drag: 54 lbf at 40 mph
 Weight: 30 lbs
 Improve aerodynamic efficiency of rear wing in dynamic yaw situations (β°)
 Improve the carbon fiber layup process to make the carbon fiber parts stronger and lighter
Flow over the tires:
The tips’ main aim is to deflect the flow from the front tires. The tires influence the air flow in a way that
the air close to the tire surfaces may be a reverse flow compared to the overall flow coming from upstream.
The tires are the devices that might be responsible for the biggest production of drag if the flow is not
deflected around them. Therefore the aim is to deflect the flow from the tires so that the less air reaches the
tire surface.
Because of their shape and the fact that they are stuck to the ground, the tires create lift. Considering
an infinite wide stationary cylinder, the flow pattern would be the following: the particles of air would be
accelerated on the upper surface and would not be able to go through the lower one as the cylinder is
assumed to be stuck to the ground. The flow would separate at around 160 degrees from the stagnation
point. This means that the flow remains attached along a great distance and that the pressure coefficient
becomes more negative on the upper surface because of the higher speed induced: in theory, the speed of
air is doubled at 90 degrees from the stagnation point on the upper surface. This results in additional lift as
it is the upper surface but it results too in additional drag as this negative pressure area is mostly located

21. 21
behind the middle of the wheel. Then, as the tire rotates, the separation point goes forward. This destroys
the original lift generated by the tire and the drag generated by low pressure surface too. However drag is
very high because of the separated flow behind the wheel.
About the flow pattern, the tires modify the flow due to their rotation. In front of them, the flow tends to go
down and the stagnation point gets closer to the ground as the rotation speed increases. So the flow separates
in two sub flows at the stagnation point. The lower one is confronted to the wheel in front of it and to the
ground below it. A recirculation area forms and the flow escapes on the sides.
Since in Formula SAE the front wing can be as wide as the widest point of the tires, in order to reduce
the drag generated by the tires, the flow will be forced to go around the tires.
Rear Wing Optimization
Flow pattern around a tire

22. 22

23. 23

24. 24
Shear strength calculations
𝑆 𝑡𝑒𝑛𝑠𝑖𝑙 𝑒 = 𝐴 ∗ 𝑡 𝑚𝑖𝑛
Where 𝑆 𝑡𝑒𝑛𝑠𝑖𝑙𝑒 is the ultimate tensilestrength,A isthe affectedareaof the bolt,and 𝑡 𝑚𝑖𝑛 is the minimumtensile
strengthgivenbythe manufacturer.Setting 𝑡 𝑚𝑖𝑛=170,000 psi and A=0.017 in2
fora number10 bolt,andA=.0091
for a number6 bolt
𝑆 𝑡𝑒𝑛𝑠𝑖𝑙𝑒 = 0.017 --𝑖𝑛2 ∗ 170,000 𝑝𝑠𝑖
𝑆 𝑡𝑒𝑛𝑠𝑖𝑙𝑒 = 2890 𝑙𝑏𝑓
Basedon The Industrial FastenerInstitute (InchFastenerStandards,7th
ed.2003. B-8), the ultimate shearstrength
can be estimatedasbeing60%of the ultimate tensilestrength.Therefore,the ultimate shearstress( 𝑆 𝑠ℎ𝑒𝑎𝑟) can
be estimatedas:
𝑆 𝑠ℎ𝑒𝑎𝑟 = 0.6 ∗ 𝑆 𝑡𝑒𝑛𝑠𝑖𝑙𝑒
𝑆 𝑠ℎ𝑒𝑎𝑟 = 0.6 ∗ 2890 𝑙𝑏𝑓
𝑆 𝑠ℎ𝑒𝑎𝑟 = 1734 𝑙𝑏𝑓 for number10 bolt
𝑆 𝑠ℎ𝑒𝑎𝑟 = .6 ∗ 0.0091 𝑖𝑛2 ∗ 170,000 𝑝𝑠𝑖 = 928𝑙𝑏𝑓 for number6 bolts
Reusable Shankless Rivets
The above-mentionedfastenerswerechosenbecauseof theirease-of-use,cost,andweight.Inordertoensure
that these fastenerswere,astested,able tolive uptothe harshenvironmentthata car demands,theywere
testedinstandard-sizedholesof .25”
The holeswere drilledwithcare,butthere wasminorvariance inthe way the holeswere drilledsuchthatthe
holeswere neversupremelycircular.Thisallowedforvariance inthe diameterof the hole andthuslythe pinch
neededbythe shankinorderto be pushed-inorpulledout.A teststandwasmade to holdcertainsamplesof
carbon fiberthatwere usedtoassemble the bodywork,andthisteststandwas placedupona scale whose
measurementsare inincrementsof .5 𝑙𝑏𝑓.The loadswere appliedbyhandina directionsnormal tothe plate
that holdsthe carbon strips,asshowninFigure 1
The test setupisshowninfigure 1 withthe carbon fibersample andthe rivet:

25. 25

26. 26

27. 27
Trial 1 Trial 2 Trial 3 Trial 4 Trial 5
Pull
(lbf)
Push
(lbf)
Pull
(lbf)
Push
(lbf)
Pull
(lbf)
Push
(lbf)
Pull
(lbf)
Push
(lbf) Pull (lbf)
Push
(lbf)
10.5 4.5 13 6 14.5 6.5 13.5 6 18 5
15 5 10.5 5.5 13 5 11 6 16 8.5
11 4.5 11.5 6 13.5 5 12.5 5.5 9.5 5.5
14.5 6 11 5.5 11 4.5 12 6 5 5
12 5.5 11 5.5 10 4.5 13.5 5 9 5.5
Average 12.6 5.1 11.4 5.7 12.4 5.1 12.5 5.7 11.5 5.9
Std.Dev 1.827567 0.583095 0.860233 0.244949 1.655295 0.734847 0.948683 0.4 4.795832 1.319091
Push Pull
Total
Avg. 12.08 5.5
Total
St.D 1.440002 0.370329
Tension Wire calc:
Assuming304 SS for Durasteel Wire constructionbyOOk,
𝜎 𝑦 = 32000 𝑝𝑠𝑖
𝐸 = 28000 − 29000 𝑘𝑠𝑖
%𝐸𝐿 𝑏𝑟𝑒𝑎𝑘 = 70%
 𝐴𝑟𝑒𝑎 𝑐𝑟𝑜𝑠𝑠−𝑠𝑒𝑐𝑡𝑖 𝑜 𝑛𝑎𝑙 = 𝜋 (
𝑑
4
)
2
= 𝜋(
.060
4
)
2
≈ 𝟐. 𝟖𝟑 ∙ 𝟏𝟎−𝟑 𝒊𝒏 𝟐
 𝜎 𝑎𝑝𝑝𝑙𝑖 𝑒𝑑 =
𝐹𝑎𝑝𝑝𝑙𝑖𝑒𝑑
𝐴𝑟𝑒𝑎 𝑐𝑟𝑜𝑠𝑠−𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙
=
50𝑙𝑏𝑓
2.83∙10−3 𝑖𝑛2
= 𝟏. 𝟕𝟕 ∙ 𝟏𝟎 𝟑 𝒑𝒔𝒊
𝑭. 𝑺 =
𝝈 𝒚
𝝈 𝒂𝒑𝒑𝒍𝒊𝒆𝒅
=
𝟑𝟐𝟎𝟎𝟎𝒑𝒔𝒊
𝟏𝟕𝟕𝟎𝟎𝒑𝒔𝒊
= 𝟏. 𝟖

28. 28
For an installationlengthof _20.5_ in,and a strain to yieldof .002:
𝜖 =
𝑙 𝑜 − 𝑙
𝑙 𝑜
=
𝛿𝑙
𝑙 𝑜
= 0.002
𝜹𝒍 = 𝒍 𝒐 ∙ 𝟎. 𝟎𝟎𝟐 = 𝟐𝟎. 𝟓 ∙ 𝟎. 𝟎𝟎𝟐 = . 𝟎𝟒𝟏 𝒊𝒏
%𝑬𝑳 𝒃𝒓𝒆𝒂𝒌 = . 𝟕 ∗ 𝟐𝟎. 𝟓𝒊𝒏 = 𝟏𝟒. 𝟑𝟓 𝒊𝒏
Simulation numbers
75 mph downforce (lbf) drag (lbf)
Front WingMain 192.3 9.5
Front Wing2nd 13 12.3
Rear WingMain 141.8 37.5
Rear Wing2nd 27.2 28.2
Undertray 68.4 20.6
Column1 Downforce (lbf) Drag (lbf) Efficiency
Full car 141 67 2.1044776
Front
wing
64.9 11.78 5.5093379
Rear wing 52.5 20.1 2.6119403
Undertray 33.3 7.2 4.625
Nosecone 1.1 3.96 0.2777778
Side-pods -2.2 1.7 -
1.2941176
Front
tires
-2.1 2.56 -
0.8203125
Rear tires -2.7 6.4 -0.421875
C_L C_D
Full car 0.72 0.342