1. DRAG FORCE AND COEFFICIENT
VALUES
FOR SEDAN RANGE VEHICLE
PROFILES
Muhammad Firdaus bin Kosnan
(2013262704)
Dr. Kausalyah a/p Venkatason
ABSTRACT
Nowadays demand of a high speed car is increasing in which vehicle
stability is of major concern. Forces like drag, lift, weight, side forces and
thrust acts on a vehicle when moving on road which significantly affect the
vehicle performance and safeness of traffic users. The drag force is produced
by relative motion between air and vehicle and about 40% of total drag is
produced at the front-end. Around 84% of all pedestrian fatalities involve
frontal impacts and it is found that the vehicle front-end structure plays a key
role in the determination of severity of injuries. Reduction of drag force at
the front-end improves the capabilities of car also to decrease the fatality
risk. This work aims to reduce the drag force which improves vehicle
performance and protects pedestrians as well. In the stage of work a sedan
car with different types of dimensions are used to reduce the aerodynamic
drag force. The design of sedan car has been done on Solidworks and the
optimization front end vehicles protection data is taken from previous
research. The analysis is done for finding out drag forces at different
dimensions on frontal area and compares it with the safety values
requirement.
Keywords: Drag force, front end vehicles
Introduction
Drag is force acting opposite to the relative motion or any moving object,
particle and substance with respect to a fluid or air. It acts parallel and same
direction as the airflow. Drag force always decrease fluid velocity relative to
the solid object. When objects move, they quickly build up forces in the
opposite direction; these are usually air resistance (drag) and friction forces.

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Drag force is proportional to the velocity for a laminar flow and the squared
velocity for a turbulent flow. Even though the ultimate cause of a drag is
viscous friction, the turbulent drag is independent of viscosity.
In vehicle aerodynamics, drag is comprised fundamentally of two
forces. Frontal pressure is caused by the air aiming to flow around the front
of the car. The front grill of the car having a millions of air molecules
approaching, they begin to compress, and due to this the air pressure in front
of the car will raise. Simultaneously, the air molecules moving along the
sides of the car are at atmospheric pressure, a lower pressure compared to the
molecules at the front of the car.
Figure 1: Air pressure increases in front side of car
Drag is caused at the nose of the car by air molecules hitting the
front bumper, and at the rear of the car as air coming off the wing creates a
partial vacuum that literally sucks the car backward. Unfortunately, there is
no aerodynamic force that pushes the car forward. All of that force has to
come from the engine. Note that the air usually exerts a force at an angle, so
that, for example, the force on the hood is made up of some drag and some
down force.
The drag equation is a formula used to calculate the force
of drag experienced by an object due to movement through a fully
enclosing fluid. The formula is accurate only under certain conditions: the
objects must have a blunt form factor and the fluid must have a large
enough Reynolds number to produce turbulence behind the object. The
equation is
where is the density of the air and is the exposed area of the operating
object; or else, is the cross-sectional area perpendicular to the direction of
motion. The direction of velocity is always opposite to the direction of the

3. 3
drag force. stand for flow velocity in the direction normal to the plane.
Drag coefficient, is a dimensionless quantity that is used to specify the
drag or resistance of an object in a fluid environment, such as air or water [1].
Literature Review
Aerodynamic in Automobile
As automobile technology develops, the speed of automobiles is increasing.
Thus, the aerodynamic performance becomes crucial because aerodynamic
drag is proportional to the square of the speed. Additionally, a reduction of
the aerodynamic drag is achievable at a relatively low cost compared with
developing a more efficient power train system [1]
Many attempts have been made since the early years in the
automotive industry to reduce aerodynamic drag in order to improve
performance and fuel economy. A theoretical method had established to
determine the shape of passenger car body for minimum drag by imposing
the condition that the total lift be zero. With this condition and a gradual
variation in the area and shape of transverse cross sections of the body, a
basic shape was achieved with a drag coefficient of 0.23. This research
proved that the aerodynamic drag can be minimized substantially with an
improved body shape without any additional devices [2]
Table 1: Basic criteria for automotive aerodynamic design [2]
If the power of the engine wants to be fully played to enhance the
dynamic performance of the vehicle, for most of the time, down-force
generated by aerodynamics package is necessary to provide enough adhesion
force. The wind-averaged drag coefficient CD is a variable that depends on
crosswind effects and vehicle speed and requires detailed data of regional
wind statistics [3].
The aerodynamics of the vehicle seems less important compared to
its dynamic performance; however, the aerodynamic performance of a race

4. 4
car will have an effect on the overall performance of the vehicle. With the
increased tendency in the automotive market to high powered and compact
engines, the necessary underhood air flow for engine cooling has been
accompanied by an increase in drag and lift values. It is commonly known
that resulting changes are due not only to the resistance of the internal flow
but to several other effects as well. The contribution of single vehicle
components to the change in integral coefficients is not fully understood [4].
There are several contrasts in automotive aerodynamics and aircraft
aerodynamics. First, the shape of a road vehicle’s element is slighter
streamlined compared to an aircraft. Second, the vehicle controls above the
ground rather than in free air. Third, the driving speeds are slower than flying
in surrounded air and aerodynamic drag varies as the square of speed. Fourth,
a ground vehicle has a small number of degrees of freedom than the aircraft,
and its motion is less influenced by aerodynamic forces. Fifth, road vehicle
and automotive have very specific design constraints such as their intended
purpose, high safety standards, for example, more 'dead' structural space to
act as crumple zones and certain regulations.
Crash safety value
Pedestrians are exceedingly unsafe road users who are at high injury riskiness
in road traffic accidents with motor vehicles. These pedestrian afflictions
pose a serious problem throughout the world. These averages to one crash-
related pedestrian death had been determined according to National Highway
Traffic Safety Administration (NHTSA). By the increasing number of traffic
accidents, every 2 hours foot traffic died and a pedestrian injury in every 8
minutes [5]
Literature shows that about 84% of all pedestrian fatalities involve
frontal impacts and it is found that the vehicle front-end structure plays a key
role in the determination of severity of injuries [6]. Furthermore data
compiled from the Malaysian Institute of Road Safety Research indicate that
40% of all pedestrian motor vehicle crash casualties involve children aged
between 6 and 10 years old [7].
Advances have been made by vehicle manufacturers to address this
issue with respect to the design of the vehicle, but the complex nature of the
pedestrian accident scenario has resulted in difficulties in optimizing the
design. The shape of the vehicle front end has shown to contribute as the
leading factor in determining the pedestrian kinematics, which in turn affects
the injury outcome, primarily that of the head [8]. The shape of a vehicle’s
front-end, traditionally designed according to style, aerodynamics,
manufacturability, engine packaging and occupant safety, has been shown to
be the most important vehicle design-related factor in determining pedestrian
kinematics, which in turn, determines the impact speed, impact angle and
location of head impact, ultimately affecting the injury outcome [9].

5. 5
Methodology
Figure below shows the parameter which been used to estimate the range of
vehicle to make it various and performed as a frontal-end area of car. A
sample of a vehicle front-end geometry for which there exists a set of
validation test data, is adopted from literature [10]. Figure 2 shows the front-
end geometry profile and dimensions. These, as well as the weight, centre of
gravity and material properties are maintained as closely as possible, based
on the Ford Taurus detailed FE model, developed by EASi Engineering for
the National Highway Traffic Safety Administration (NHTSA) [11]
Figure 2: Vehicle front-end design parameters and profile shape [11]
Table below shows a few plans of experiments for the central
composite design for the front-end geometry of sedan car. The experiment
consists of 72 models with different values of geometry and dimension.
Table 2: Design matrix (Orthogonal, Faced)
The process of modelling the vehicle profile be made of several
steps. Sketching is the first step of the drawing the model. Sketching in

6. 6
Solidworks is uncomplicated and simple cause they provide with quite a lot
of necessary steps which is lines, perimeter circle, corner rectangular, tangent
arc and straight slot. Beside they got rapid sketch features which allow the
two dimension sketch plane to change dynamically
Figure 3: Full drawing of the model with the dimension
Figure 4: Three dimension shape using extrude boss features
The model fabricated from Solidworks then being tested for the
airflow and the force value generated. The setup has been made before

7. 7
running the simulation. This analysis only uses external flow only.
Solidworks Flow Simulation automatically considers all closed cavities
within the model as filled with the fluid. Exclude cavities without flow and
exclude internal space option will remove the fluid regions not relevant for
the problems from the analysis.
Figure 5: Analysis type and reference axis selection menu
In a wind tunnel testing, the car is assumed to be at stationary while
air is moving. This condition is applied similarly in Solidworks Flow
Simulation where it is highly regarded as a virtual wind tunnel. Therefore,
positive value of 22.22m/s in Z direction is appropriately represented the flow
boundary
Figure 6: Wizard-Initial Conditions system box with 22.22m/s velocity in
Z direction
After run that wizard’s setup, Solidworks Flow Simulation has
calculated the goals for this experiment. By adjusting the Flow Trajectory,
the flow become visible to be shown and total calculation has been tabulated.

8. 8
Graph represents the Force (N) over Iterations which can be modified
according to the experiment purpose.
Figure 7: Flow Trajectory and calculated data represent after simulation
is done
Figure 8: Graph plotted with Force (N) versus Iteration
Result and Discussion
Optimal result of force
Based on the analysis that had been performed, the best rate of force produce
is classified in form of the smallest to the largest value. Later, the

9. 9
classification the data is narrowed down until it reach a best 5 out of 79 runs
of the flow simulation.
NO
DRAG
FORCE (N)
DRAG
COEFFICIENT (N)
15 120.789 0.135
27 115.512 0.143
5 132.088 0.141
23 140.405 0.150
9 118.135 0.186
Table 3: Best 5 out of 79 runs of the simulation
Comparison between final combined optimised model
From the multiple optimisation of front end vehicle, an adult and child
pedestrian friendly vehicle shape is obtained. The design has an abilities to
avoid run-over scene plus improved protection for adult and child pedestrian.
The tabulated data of physical design parameters of vehicle are presented in
Table 4. Meanwhile the vehicle front-end profile shape is illustrated and it
can be seen that run over scenario is terminated. In addition, the HIC values
for both the adult and child are 209.34 and 195.47.
Table 4: Design parametes of final combined optimized design with Run-
over event consideration

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Figure 9: Vehicle front-end profile geometry of final combined optimized
design with Run-over consideration
In the meantime the design parameter value is redesigned and
simulate it into flow simulation process to identify the force acting on the
surface area of the object. In addition to the crash kinematics analysis with
run-over consideration, the aerodynamic of the car need to be examine as
well to ensure the stability while on the road and the fuel consumption of the
design.
The average of the design parameter state at design 37 according to
the final combined optimisation result. The result of the analysis is tabulated
on Table 5.
Design
parameters
Combine
Optimised
Model
15 27 5 23 9
x1 +1 -1 -1 -1 -1 -1
x2 -1 -1 +1 -1 +1 -1
x3 -1 +1 +1 -1 -1 +1
x4 +1 +1 -1 +1 +1 -1
x5 -0.479 +1 +1 -1 +1 -1
x6 -1 -1 -1 -1 +1 -1
x7 +1 -1 -1 -1 +1 -1
Drag (N) 228.718
120.78
9
115.51
2
132.08
8
140.40
5
118.135
Coefficient
(N)
0.268 0.135 0.143 0.141 0.150 0.186

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Table 5: Drag and coefficient value for best 5 and C-opt model
The observed force value for both the drag force and drag coefficient
for Combine Optimised Model according to Table 5 are 228.718 N and 0.268
N, respectively. By the estimated design, the value of drag force and
coefficient is not in the best result beside the design has high amount of
forces compare to the top 9 optimal performance ranking. In spite that the
value is not achieve the requirement of the ideal drag, the final optimised
shows the great implementation of avoiding hit and run scenarios which
equally satisfied for both adult and child pedestrians.
Table 5 shows the x1 value has negative value for most of the
design. It shows the windshield angle has lower value and create an inclined
shape. For bumper lead, x2 either more or very little length while x6 and x7
mostly its recorded low value. Its means less angle are use in x6 and x7.
Literally the designs tends to have a shape of airfoil due to the low value of
drag and coefficient force. Based on fill the combination, the profile that
works towards goes inclined towards more the airfoil shape actually. The
nature of the choices of optimisation when it comes to the drag coefficient is
actually going towards as airfoil shape which can be seen in Figure 11.
Meanwhile, between 0.135 and 0.186 value, there have a similar
number as the drag coefficient of a sporty cars. Naturally sports cars have
interest to get high speed and low drag but not in pedestrian safety. So that
the cars are not for the purpose of main street but in racing course.
Therefore, what has been chosen up as optimised for the drag efficiency are
those types of cars.
Figure 10: Line graph based from coded value

12. 12
It is observed that clearly different shape of design produce a various
type of crash patterns for adult and child. This situation same goes to the
production of force regarding to the result obtained from flow simulation.
Frontal area of vehicle can be reduce by decreasing the height and width but
the consideration of effect of crashing with pedestrian need to highlight due
to a lot of accidents occurs by ran over the foot traffic causes by irresponsible
motorist. While the car travelling at speed just beyond the limit, the victims
have probability to pitch forward to the hood and it continue by the victim’s
head will strike a windshield.
Figure 11: Vehicle profiles for best 5 and C-opt model
Figure above shows the vehicle profiles of final combined optimised
model from previous research and 5 best design. In the DOE setup, 5 best
designs were chosen which has minimised Cd. It has not been confirmed
whether these designs will give low Head Injury Criterion (HIC) values.
Besides it is acceptable if the HIC rises approximate 200 values above the
optimised value for both adult and child which will mean that the injury is
still within treatable range.

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According to the previous research, when the HIC comes to the
range of 200 to 300, the victims may well produce fatal injury and suffering a
concussion while 400 to 500 value will probably having a permanent
disability, coma and fluid retention [12]. Therefore, an important
consideration that current vehicle engineers take into reminder list while
designing car is crash safety factor beside this can be further studied to
develop more HIC value, respectively.
This is natural considering the affect will bring at drag force, where
more airfoil shape will actually minimize the drag. Nevertheless the
combined optimised profiles has well recorded drag force and coefficient as
well. For those where the drag value is very low, the injury criteria is needed
to study
Conclusion
To sum things up, various vehicle front-end design parameters and profile
shape lead to the various external force act parallel and the same way of
airflow. Aerodynamics are one of the key area of improving system in
stability, performance and fuel efficiency. The main balance is to get more
drag reduction and maximize the stability of car while moving straight or
cornering in a certain speed. These profiles are taken from sample of existing
cars in Japan, US, Europe, and Korean market. This allow the drag
coefficient values fall within the permissible range. In fact that the average
of modern cars having a drag coefficient between 0.3 and 0.35 while normal
boxy shape automobile achieve a drag coefficient of Cd = 0.35-0.45. The
variation of Cd value not only depending to the frontal area, it will vary rely
on which wind tunnel it is measured in. In short if the same vehicle having a
Cd = 0.34 and tested to a different tunnel it could be in any place from Cd =
0.30 to Cd = 0.40.
For further study, there are plenty of new elements that automakers
can put into practice to bring down the drag coefficient of vehicles. New
improvements of wind tunnels and development in simulation software are
used to obtain more precise value of drag. The effects of particular vehicle
shape on the aerodynamics of a car can be estimated by using calculation of
equations to explore the fluid dynamics of air flowing around a vehicle.
Therefore further study need to be carried out following the best optimised 5
based on discussion that already made.
References
1. Howell, J. S. (2002). Aerodynamic drag of a compact SUV as
measured on-road and in the wind tunnel. (2002-01-0529).

14. 14
2. Morelli, A. F. (1976). The Body Shape of Minimum Drag.
Warrendale: SAE Technical Paper 760186.
3. Mohamed-Kassim Zulfaa, A. (2010). Fuel savings on a heavy
vehicle via aerodynamic drag reduction. Transportation Research
Part D , 275-284.
4. Mahmoud Khaled, H. E. (2012). Some innovative concepts for car
drag reduction: A parametric analysis. Journal of Wind Engineering
and Industrial Aerodynamics , 36-47.
5. Howell, J. S. (2002). Aerodynamic drag of a compact SUV as
measured on-road and in the wind tunnel. (2002-01-0529).
6. Morelli, A. F. (1976). The Body Shape of Minimum Drag.
Warrendale: SAE Technical Paper 760186.
7. Mohamed-Kassim Zulfaa, A. (2010). Fuel savings on a heavy
vehicle via aerodynamic drag reduction. Transportation Research
Part D , 275-284.
8. Mahmoud Khaled, H. E. (2012). Some innovative concepts for car
drag reduction: A parametric analysis. Journal of Wind Engineering
and Industrial Aerodynamics , 36-47.
9. Howell, J. S. (2002). Aerodynamic drag of a compact SUV as
measured on-road and in the wind tunnel. (2002-01-0529).
10. Teng, T. L., Le, T. K., & Ngo, V. L. (2010). Injury analysis of
pedestrians in collisions using the pedestrian defomable model.
International Journal of Automotive Technology , 187-195.
11. Wu, C. C. (2003). The analysis of occupant injury in frontal impact
of traffic accident. M.S Thesis , 187-195.
12. 2] G. Bronwyn, W. Kerrianne, W. Belinda, S. Linda, and K. Roy,
Paediatric low speed vehicle run-over fatalities in Queensland, Inj.
Prev. 17(Suppl 1) (2011), pp. i10–i13.