Effect of the Aerodynamic Elements of the Hatchback Tailgate on the Aerodynamic Drag of the Vehicle

The paper deals with the possibilities of reducing aerodynamic drag and modifying airflow in the rear of a hatch - back vehicle. This body type is characterised by the formation of turbulent flow behind the vehicle, which has a significant effect on the fouling of the tailgate, including the window. By modifying the geometry of components such as the roof spoiler and additional aerodynamic finlets on the sides of the rear window, the airflow is optimised to reduce aerodynamic drag and thus fuel consumption. Three spoiler designs are proposed, one of which is pro - cessed to prototype quality using CAD tools. The body of the vehicle with this design is subjected to CFD analysis and evaluated in terms of the given criteria. The results of the simulations are compared with a model of a produc - tion vehicle and a sports version vehicle to assess the effect of the geometry on the flow parameters.


INTRODUCTION
Aerodynamics deals with the flow of air or other gas and the way in which objects such as airplanes, cars, turbine blades and the like pass through these media. As these objects pass through the air, there is a mutual reaction and thus a change in flow. The findings from the analysis of the flow around the objects are used mainly by the aerospace and automotive industries. When the aviation industry is mainly concerned with providing the lift needed to fly an aircraft, in the automotive industry it focuses on reducing aerodynamic drag. At a time when European legislation by emission standards is pushing motor vehicle manufacturers to reduce emissions, aerodynamics is being offered as one of the ways to achieve the required emission values given by legislative requirements. Saving every gram of fuel makes sense. One way to reduce fuel consumption and emissions is to make a significant contribution to improving vehicle aerodynamics, as at speeds above 100 km/h, aerodynamic drag represents the greatest drag of a moving vehicle.
The influence of aerodynamics is already visible in the beginnings of the automotive industry. This is evidenced by Camille Jenatzy's torpedo-shaped vehicle, which in 1899 exceeded a speed of 100 km/h [1]. This period in the late 19th and early 20th centuries can be called the first phase of the application of aerodynamics in car design, when designers sought inspiration in the product shapes of other technical fields. They were inspired by e.g. airships from the air force or the already mentioned military torpedo. The second phase in the development of vehicle aerodynamics dates to the 1930s, when the automotive designer Paul Jaray, inspired by the shapes of the jets, purposefully creates the bodies of the so-called jet shape. One of the most famous designs are the TATRA 77 (1934) and TATRA 87 (1937) cars [1].
His successor Wunibald Kamm creates the BMW 328 from 1940. Not to mention the Effect of the Aerodynamic Elements of the Hatchback Tailgate on the Aerodynamic Drag of the Vehicle Michal Fabian 1* , Róbert Huňady 1 , František Kupec 1 , Tomáš Mlaka 2 1 Faculty of Mechanical Engineering, Technical University of Košice, Letná 1/9, 042 00 Košice, Slovakia 2 D.G. Engineering; Sládkovičova 5, 984 01 Lučenec, Slovakia legendary VW Beetle by Ferdinand Porsche, which began to develop in 1931. For us, the modern third phase of vehicle aerodynamics, which is focused on optimizing body details dates to '70s of the 20th century. The design of vehicles of this stage is focused on maximum functionality and efficiency. Janseen and Hucho in [2] describe the optimization of Volkswagen Golf Mk.1 and Scirocco Mk.1 body details. Hucho then publishes his findings in [3], where he deals with the issue of body optimization in wind tunnels. In the summary publication [2] Hucho describes the history of the implementation of aerodynamics in the construction of car shapes and summarizes the theory in this area. The seventies of the twentieth century deal not only with reducing aerodynamic drag, e.g. Marte et al. [4], Morelli et al. [5] and Shibata et al. [6] but other problems related to aerodynamics such as aerodynamic noise are also beginning to be investigated. The issue of aerodynamic noise is dealt with e.g. Chanaud and Muster [7].
Furthermore, the relationships between aerodynamics inside the engine compartment, which are discussed by Emmelmann and Berneburg in [8], and the impact of aerodynamics on emission reduction, which are discussed by Rouméas et al. in [9], are being investigated. The named authors and their work should be taken as a selection of the best known, because many other scientists and entire development teams of automobiles also deal with this issue.
With the advent of computer technology and simulation software, experiments from wind tunnels have been transferred to computer laboratories. Most calculations are performed on virtual car models. Shankar and Devaradjane [10], Chode et al. [11] and Song et al. [12] address this issue. In 2016, Thomas Schuetz and his team published 26 co-authors, one of whom is W.H. Hucho monograph [13], in which he summarizes the current theory of aerodynamics and expands it with modern simulation calculation methods CFD (Computational Fluid Dynamics), which simulates aerodynamic calculations in a virtual computer environment. Katz deals with the issue of aerodynamics in motorsport in [14]. Kumar et al. [15] discussed the optimization of specific car parts. They performed a comprehensive analysis of the vehicle with aerodynamic optimization of the shape of the rear bumper with the air duct at angles from 0° to 13°. According to the results, at certain angles, the wake region behind the vehicle was reduced and thus the aerodynamic drag decreased from 0.3454 to 0.2322. The best results were obtained with a 12° angle of inclination of the air channel. The analysis was performed by CFD software ANSYS Fluent.
Modifications to the rear of the car using spoilers, added slats and their effects on the overall air resistance of the car have also been discussed by several authors. Hamut et al. in [16] dealt with the effect of rear spoilers on the aerodynamic drag of a land vehicle. The effects of the diffuser position in the floor of the rear of the car and the effect on the lifting and resistance force at 60 km/h with angles of 10º, 15º, 20º and 30º were investigated by Baek et al. in [17]. In dissertation thesis [18], Mustafa C. investigated the aerodynamic effects of a car rear spoiler on a passenger car using the CFD method. Ferraris A. et al. in [19], by optimizing the shape of the elements and adding individual shapes to the whole body, they devoted themselves to the modification of the experimental car XAM 2.0. They obtained their results using the CFD method, while also correlating between the results of virtual and experimental analysis in the Pininfarinna wind tunnel. Salama Y. et al. conducted an aeroacoustic study, which they present in [20]. Using wind tunnel testing, they analyze the impact of ribs and finlets on aeroacoustic properties and determine the positive impact on reducing the broadband noise emitted by the profiles.
Currently, the production of a single model of a European vehicle takes at least 8 years. During this production period, vehicle manufacturers are forced to adapt to the requirements of reducing emissions and increasing vehicle efficiency, which adds to the development and production costs. Thus, opportunities for additional body modifications to reduce the air drag coefficient are provided by facelifts. These are mainly modifications to some exterior components to make them cost-effective. The design changes therefore mainly concern plastic parts, as they are cheaper to produce than sheet metal parts.
This paper presents how the process of modifying the selected components is carried out. The aim is to modify the airflow behind the vehicle in order to reduce the aerodynamic drag of the vehicle and thus increase its efficiency. In the case at hand, this flow will be guided by modifying the spoiler and adding side finlets, which are part of the rear doors of the vehicle. In addition to reducing the vehicle's drag, a secondary beneficial eff ect is to move the air further away from the vehicle along its length, resulting in a reduction in pollution of the rear window of the tailgate.

AERODYNAMICS OF ROAD PASSENGER VEHICLES
A vehicle moving on the road is exposed to various resistances. The total resistance of a moving vehicle is the sum of rolling resistance, acceleration resistance, gravity, and air drag. In order to moving of the vehicle forward, it is necessary to overcome these resistances.
The value of the air drag coeffi cient c D is used to calculate the air drag. Air drag depends not only on the shape of the body, but also on other factors, such as its size, surface roughness, air density, velocity, but also the fl ow, whether it is laminar or turbulent. Individual body shapes have diff erent coeffi cients of air drag, while a body with a circular cross-section has a drag coeffi cient of 0.47, a cube-shaped body has a drag coeffi cient of 1.05, but if we rotate this body by 45° so that the edge of the cube faces forward, the drag coeffi cient decreases to 0.8. A body that has a jet shape (tears or drops) has a drag coeffi cient of only 0.05 [21]. The individual shapes and their coeffi cients of air drag are shown in Figure 1.
The aerodynamic properties of vehicles are a consequence of aesthetic economic and functional properties. The performance, handling and comfort of road passenger vehicles are significantly aff ected by the aerodynamic properties of vehicles. Low air drag is a prerequisite for lower fuel consumption. But the other aerodynamic properties of vehicles are not negligible and depend on the air fl ow around the vehicle. These features include, for example: crosswind stability, wind noise, body, headlight or glass contamination, engine, transmission and brake cooling, and fi nally interior heating and ventilation.
At lower speeds, the rolling resistance of the rolling wheels of the vehicle is also dominant. The wider the tires, the greater the contact area with the road and the greater the rolling resistance. However, in addition to the aerodynamic drag of the vehicle, it can simply be said that rolling resistance is constant if we do not take into account the change in driving conditions. The dependence of rolling resistance and air drag of the vehicle (Fig. 2) shows the signifi cance of the increasing resistance caused by the aerodynamic properties of the vehicle. The air drag increases with the square of the vehicle speed, so at speeds above 100 km/h (speed may vary depending on the specifi c vehicle) it becomes dominant [22,23].
Aerodynamics deals not only with external fl ow, but also with problems of internal fl ow systems. Because the outer and inner current fi elds are interconnected, and both must be considered at the same time.
According to the laws of fl uid mechanics, motor vehicles are considered to be surface objects located in close proximity to the road. Their detailed geometry is very complex, provided by a number of holes and cavities, such as the engine  compartment or the vehicle fairing, which are connected to the external airflow and, together with the rotating wheels, increase the complexity of the airflow. The airflow around the vehicle is fully three-dimensional. Turbulent flow is created at vehicle surfaces. Large turbulent flow is created in the rear of the vehicle and in many cases contains large end air vortices.
Another equally important task that aerodynamics provides is engine cooling. The direction of air flow to the radiator is determined by the air flow at the front of the vehicle. The grille must be designed to direct the air into the radiator, while maintaining the least possible pressure loss. The flow in the area of the hood and windscreen can be used for heating and ventilation system. Therefore, most vehicles have a fresh air supply in this area.

BASIC PRINCIPLES OF CAR AERODYNAMICS
External airflow affects vehicles. Forces and moments are created here that affect the performance and stability of the vehicle. Until recently, vehicle aerodynamics have only focused on these two effects, and only recently has it focused on the need to prevent pollution of windows and lights, noise reduction, brake cooling, oil pan cooling, etc. In Fig. 3 we can see an example of the air flow, where some factors can be identified, such as the tear-off of the air flow at the rear of the vehicle in Figure 6.
The aerodynamic drag D of the vehicle increases with the square of the vehicle speed. It can be calculated as follows where: A x is the reference (cross sectional) area of the vehicle, c D is the air drag coefficient, ρ is the air density, ν F is the cruising speed.
In general, the reference area depends on the design requirements of the vehicle body type and is determined by the projection of the vehicle in the direction of travel (Fig. 4). The air drag coefficient is a number used to describe all the complex dependencies of shape, slope, and flow conditions on drag. This coefficient is influenced not only by the car body but also by the chassis, wheels, tires, and rear-view mirrors. Therefore, if a larger SUV has better aerodynamics and therefore a lower air drag coefficient, it may not have lower drag than a smaller car due to its larger frontal area. Efforts to reduce air drag are focused on reducing the air drag coefficient. For currently manufactured cars, the values of the air drag coefficient of cars range somewhere between 0.2 and 0.4 [1].
The air drag of a European mid-size vehicle is almost 75 to 80% of the total resistance of the vehicle at a speed of 100 km/h. This creates scope to improve fuel consumption by improving the aerodynamics of the vehicle. In essence, this is a direct reduction in the air drag of the vehicle by modification its external parts. However, the aim may also be to improve dynamics, as better aerodynamics of the vehicle will reduce the power required to overcome air drag.

Forces and moments acting on the car
Using the basic coordinate system of the vehicle, starting at its center of gravity, it is possible to define the forces and moments acting on the car while driving. The most dominant is the aerodynamic drag force (marked as D) acting against the direction of the vehicle. The second is the lift force (marked as L) acting upwards. This force negatively affects the stability and manoeuvrability of the vehicle, as it reduces the pressure of the tires on the road. The third is the side force (marked as Y ) acting in the direction of the Y-axis, These three acting forces are behind the formation of three moments. The fi rst of these is the pitching moment (marked as M ) acting around the Y axis. This moment causes a change in the distribution of forces between the front and rear axles, e.g. during acceleration and braking. The second is the rolling moment (marked as R ) acting around the X-axis. It is created by driving in curves or on a road that is inclined at a certain angle. The last moment is the yawing moment (marked as N ) acting around the Z axis [1].
To simplify the numerical equations, we consider the so-called "symmetric airfl ow", which is defi ned without crosswinds. This means that the angle 0 b =°. Assuming symmetrical vehicle geometry, the forces Y and the moments, R, N are also zero [1].
The components of the resultant force and moment are determined on a specifi c vehicle by measurements in wind tunnels. In cases where, for economic or other reasons, it is not possible to carry out measurements on 1:1 scale models, the aerodynamic properties shall be measured on scale models. Relevant results can be obtained thanks to Reynolds' law of similarity and fi nding the Reynolds number. The equation for the Reynolds number is as follows [ where: V ¥ is the fl ow speed, v is the kinematic viscosity of the air, l is the characteristic linear dimension (vehicle length).
It is thus possible to fi nd out other required dimensionless coeffi cients listed in Table 1. All these coeffi cients are based on the dynamic free-

Working methods
Initially, aerodynamic modifications of vehicles were carried out only on the basis of experimental approaches. Shape changes were performed on scale models or full-scale models. Cogotti in [24] describes measurements on fullsize models in the process of developing new cars in the wind tunnel of the Pininfarina research centre, including the development of a methodology for such measurements in the tunnel. Experimental measurements for various body modifications have been performed by Altinisik [25]. The aim was to fine-tune the aerodynamic properties while preserving the original design as much as possible.
Nowadays, CFD calculation programs are often used in vehicle design together with experimental wind tunnel measurements. CFD computational programs make it possible to analyse multiple models and thus achieve the optimum vehicle body shape relatively quickly and at low cost. Increased fuel prices and stricter legislative requirements to reduce exhaust emissions increase the importance of aerodynamic properties in the vehicle design process [1]. In addition, virtual CFD methods accelerate and increase the efficiency of vehicle aerodynamics. Using virtual predictions obtained by CFD simulation, problems can be identified faster and cheaper. An example is the static pressure distribution in Fig. 6, which can be used to identify areas to modify the airflow by changing the shape of the vehicle body.

Development trends
The trend in car aerodynamics is to reduce the air drag of the vehicle. The air drag coefficient c D has thus been reduced from 0.8 for vehicles of the 1920s to an average of 0.45 for vehicles of the 1970s. This improvement occurred in two phases. In the first phase, between the two world wars, the vehicles were lengthened and rounded, while retaining the characteristic design features of the time, such as the bulging fenders and lights. In the second phase, the vehicles had fenders and headlights built into the body, which greatly improved the airflow around the vehicle. The concept vehicles still created opportunities for future improvements in aerodynamics. The GM Aero 2002 and Ford Probe IV prototypes designed in the 1980s achieved air drag coefficients of 0.14 and 0.15, respectively. In the case of today's commercially produced vehicles, it is between 0.25 and 0.35. In the long term, it can be assumed that the lower limit will be reduced to 0.2 [2].

Aerodynamics of the rear body of a hatchback
The rear of the vehicle is specific in that each body variant (sedan, combi, hatchback) requires an individual shape geometry solution to achieve the desired flow. Hatchback bodies often achieve the least favourable results. For this body type, it is important to tune the trailing edge of the rear of the vehicle to eliminate turbulence behind the vehicle. The turbulent flow generated in the Table 2. Equations for calculating acting forces and moments Pitching moment Rolling moment Yawing moment Table 1. Summary of equations of dimensionless coefficients Lift coefficient Side coefficient wake region (low pressure region) contributes the formation of pressure drag, which is eventually reduces the vehicle performance and causes rear window fouling as well as aerodynamic noise. The fouling is caused by swirling dust particles and water droplets from the wheels. As can be seen in Fig. 7, these are dispersed over a larger region in the case of the hatchback.

Baseline -original model
The initial state of the upper part of the tailgate consists of a simply shaped plastic spoiler (Fig. 8). The angle between the roof line and the trailing edge is approximately 150°. This angle is based on the conceptual design of the vehicle, which depends on the dimensional requirements of the interior and luggage compartment. The individual radii and chamfers are also based on the manufacturing conditions of the component. A brake light is integrated in the spoiler.

Spoiler and finlet
The tailgate spoiler (Fig. 9) is installed in the roof section in the rear window area as an additional element to improve the flow behind the vehicle. Its function is to optimize the instantaneous separation of the airflow from the rear, to improve the overall aerodynamics and also to increase the driving stability by increasing the downforce. The spoiler is usually manufactured as a plastic component due to the need to achieve an optimum shape.
The finlet is installed as an accessory that mates with the spoiler and the side edges of the tailgate window. They are used as a pair in two pieces. The purpose of this component is to create a trailing edge located outside the rear window of the vehicle and prevent turbulent flow near the glass. In addition to improving aerodynamics, another benefit is the reduction of fouling. In practice, the finlet is manufactured as a plastic component and care must be taken in its connection to the spoiler and other body parts.

Modifications to the shape of the rear of the hatchback
In order to optimise airflow and improve aerodynamic performance, three modifications to the spoiler with fins were designed. The aim was to achieve as little swirl as possible at the rear and thus reduce the overall air drag of the body.

Design A
It is a one-piece spoiler (Fig. 9 to Fig. 11) with an integrated brake light. The design takes into account the view zone, but also the continuity of the connection between the roof and the spoiler. From the point of view of aesthetic quality, this part has been designed so as not to detract from the appearance of the vehicle and to follow the shape of the body seamlessly. The proposed spoiler is considered to be a one-piece component. It partially extends into the side walls of the vehicle, thus combining the advantages of a roof spoiler and side finlets.

Design B
It is a one-piece spoiler (Fig. 12 to Fig. 14) without brake light. Aesthetics and continuity with the original body design are also taken into account in this case. The roof spoiler, as in design A, partly extends into the side walls of the vehicle, thus combining the advantages of the roof spoiler and the finlets. At the same time, it takes on the relief of the main upper window line and further develops this shape. However, this modification suppresses the rearward view of the vehicle due to the narrowing at the top of the spoiler adjacent to the body.

Design C
It is a two-piece spoiler (Fig. 15 to Fig. 17) that contemplates the incorporation of a rear brake light. The second part of the spoiler consists of a pair of side ribs fixed along the entire height of the rear window. The design takes into account the continuity of the connection between the roof, the spoiler and the finlets. This design  also provides a good view from the rear of the vehicle. From an aesthetic point of view, it follows the line of the roof and the tailgate. The shape of the fi nlets is widened at the top for a better connection to the roof spoiler.

Comparison of designs
The proposed designs represent three diff erent options for modifying the rear of the hatchback. By confronting each model with the component's production requirements and its price, the most suitable design was selected.
Design A, after checking manufacturability, requires two directions of moulding, which increases both the diffi culty and cost of its production. Therefore, this design will not be refi ned to prototype quality.
Design B was aesthetically pleasing, most consistent with the shape of the tailgate and the rest of the vehicle, but did not meet the requirements for rearward visibility, particularly at the top of the rear window. In this case, a brake light was not incorporated. Its incorporation would have resulted in a further narrowing of the view.
For this reason, design C was selected as the most appropriate and was subjected to further investigation. Figure 18 shows the diff erence in air drag coeffi cient along the length of the vehicle for two diff erent rear body modifi cations compared to the original (production) vehicle. The diff erences were determined by simulation at a speed of 140 km/h. The red curve in the fi gure corresponds to spoiler C without fi nlets, the green curve to spoiler with fi nlets. From the result of the diff erence plot, it can be seen that the design of the rear of the vehicle not only has a local effect on the aff ected area, but also has an eff ect on the front of the vehicle, which is consistent with the theoretical knowledge of aerodynamic forces. While the drag coeffi cient increases slightly in the front wheel area, it decreases in the modifi ed area. In the case of a spoiler without fi nlets, the coeffi cient decreases locally by approximately -0.003, in the case with fi nlets the decrease is up to twice as large.

CFD ANALYSIS OF THE SELECTED DESIGN
For a better understanding of the eff ect of the rear design modifi cation on the aerodynamic performance of the vehicle, the normalized fi elds of some other fl ow characteristics are shown in    Fig. 29. All are determined at a speed of 140 km/h. In addition to the version with the modifi ed spoiler with and without fi nlets, the results for the original (production) vehicle as well as for the vehicle in the sport version are also shown for comparison. Figures 19 and 20 shows the drag distribution on the vehicle surface. The variant with the spoiler without fi nlets shows a lower drag on the rear window of the vehicle compared to the original vehicle. A slight decrease in value can also be seen at the bottom of the tailgate. An even greater decrease in drag on the rear window is achieved for the variant with fi nlets. Fig. 21 and Fig. 22 show the distribution of the total pressure coeffi cient in the section x=3400 mm, which is located in the near wake region. This plane was chosen because the wake is largest at this location. Among all the versions compared, the most signifi cant reduction in the pressure coeffi cient can be observed for the vehicle with the modifi ed spoiler with fi nlets.
From the comparison of the normalized velocity magnitude fi elds shown in Fig. 23 and Fig. 24, it is evident that the modifi ed spoiler without fi nlets has no signifi cant eff ect on the change in the distribution and magnitude of the fl ow velocity in space compared to the production version. The changes are more pronounced for the sport version and the vehicle with the modifi ed spoiler with fi nlets. As can be seen, the low-speed region becomes smaller with increasing spoiler length. Figures 25 and 26 shows the velocity streamlines at 140km/h. Both vehicle models with the modifi ed spoiler show a reduction in the fl ow velocity behind the vehicle.
The resulting air drag coeffi cient values for all vehicle models analysed are shown in Table 3. CFD simulation results show that the air drag coeffi cient is reduced by 0.0025 for the vehicle with the modifi ed spoiler without fi nlets, which leads to a saving of approximately 0.2 litres of fuel per 100 km and theoretically reduces CO 2 emissions by 0.8 g. In the case of a spoiler with fi nlets, the reduction is up to 0.0062. The estimated reduction in fuel consumption is about 0.4 l/100 km and the reduction in CO 2 is about 1.6 g (under ideal conditions). In terms of aerodynamics, the newly proposed design of the rear of the hatchback can be considered to be an improvement compared to the production version. Note that the calculation of the fuel consumption and CO 2 emission reduction values was performed based on the vehicle parameters for the WLTP cycle.

DESIGN PROCESSING INTO PROTOTYPE QUALITY
Based on the results of the CFD analysis, which clearly demonstrated the advantages of the new spoiler designs, the CAD model C of the modifi ed spoiler with fi nlets was refi ned to prototype quality. The result of this processing is the so-called Class-A surface model (also referred to as STRAK), which takes into account detailed requirements for manufacturability, aesthetics and aerodynamic performance retention. It achieves a premium level of surface quality for visible

CONCLUSIONS
The aim of this paper was to investigate the effect of the aerodynamic features of the hatchback tailgate on the aerodynamic drag of a massproduced passenger car, the Škoda Fabia III. The main attention was paid to the spoiler and side finlets. A total of three designs were proposed, of which Design C was selected as the most suitable based on an objective evaluation. This design was subjected to CFD analysis to assess the aerodynamic response of the vehicle model at a speed of 140 km/h. The parameters monitored were the aerodynamic drag, the velocity and nature of the flow, the total pressure coefficient, and the wake region. A modified spoiler model with and without finlets was analysed. The simulation results were compared with those obtained for the vehicle model in standard production version, and in the sports version. In the case of the proposed design of the modified spoiler with finlets, an improvement was obtained in all the parameters studied. The coefficient of aerodynamic drag has been reduced by 0.0062, resulting in an expected fuel saving of 0.4 l/100 km and a reduction in CO 2 emissions of 1.6 g/km under ideal conditions according to the WLTP driving cycle. The resulting CAD model of the spoiler, taking into account the technological requirements for the production of plastic parts, was converted to prototype quality.