The Design Process of an Aerodynamic Package for an FSae Car

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Race Car Aerodynamics - The Design Process of an Aerodynamic Package for the 2012 Chalmers Formula SAE Car

2013-01-0797 Published 04/08/2013

Sven Rehnberg, Rehnberg, Lucas Börjesson, Robert Svensson Svensson and Jonathan Rice Chalmers Univ. of Technology Copyright © 2013 SAE International doi:10.4271/2013-01-0797 doi:10.4271/2013-01-0797

ABSTRACT This paper describes the design process of a full aerodynamic package of a Formula SAE (FSAE) style race car. The meaning of a full aerodynamic package in this context is a front wing, a rear wing and a diffuser; the focus will however be on the wings. The vehicle for which the aerodynamic package is designed is the Chalmers Formula Student (CFS) 2012 FSAE car, but vehicle data logged from the CFS 2011 FSAE car was used during the design phase. This data was used to evaluate how the aerodynamic package will influence the behaviour of the vehicle, both in terms of lateral and longitudinal acceleration as well as fuel consumption, in order to determine whether or not an aerodynamic package can enhance the vehicle performance. The main tool used during the design process was numerical simulations (computational fluid dynamics, CFD) and special attention was paid to post-processing of these simulations. It was concluded that although the resolution of the simulations was relatively low, valuable insights on how the air flows over the vehicle was obtained using CFD. The manufactured aerodynamic package was also evaluated during precompetition testing using an on-board data acquisition system as well as flow-visualisation flow-visualisation tufts.

(1) where F where F y is the lateral force, µ force, µ is is the friction coefficient of the tyres and F and F z is the vertical load. Many teams competing in Formula SAE (FSAE) have also tried this approach, but ever since wings were first used in FSAE the debate about whether or not they aide or reduce performance has be on-going. Those in favour obviously claim that they do help and those oppose usually claim that wings will not do much in the given speed range while they do add weight and drag which will in the end reduce rather than increase the performance [2 [2]. This dilemma, whether or not wings will increase the overall performance of a FSAE racer, was considered during the design phase of the Chalmers Formula Student (CFS) 2012 car, the CFS12. Since no previous CFS car have featured wings there was no possibility of in-house benchmarking. However, vehicle performance data logged during testing and competitions from primarily the successful CFS11 was available and used to evaluate the effects of wings.

VEHICLE DATA INTRODUCTION The method to enhance the performance of race cars by adding downforce producing devices is well established and started in the 1960's when wings were first used. In short, wings enhance the effectiveness of the tyres by increasing the load on the tyres without adding the equivalent mass [1 [ 1]. The extra load increases the lateral force which can be produced by the tyres according according to the following following equation;

The CFS12 and the CFS11 are in many aspects similar. They both feature a chromoly steel tubular space frame with body panels made of TeXtreme® carbon fibre and honeycomb sandwich material. This was also used during the manufacturing of the aerodynamic package for the CFS12. The CFS12 uses push rod suspension both in the front and in rear and relies on a 600cc Yamaha motorcycle engine to provide approximately approximately 92 hp of power power at the rear wheels.


The FSAE rules of 2012 [3] regulates the outer dimensions and positions of any aerodynamic devices which had to be considered as well as the fact that the engine requires a (theoretical) airflow of 0.56 kg/s at 56 km/h which affects the design of mainly the front wing. The CFS12 can be seen, without wings, in Figure 1.

effect on the vehicles centre of gravity (CoG), roll and pitch was assumed to be small and was thus neglected. The negative effect of adding wings, mainly drag and added mass, must also be analysed in order to get a more complete picture of the effect on performance. The drag force on a body can be calculated using equation (4);

(4) where cd is the coefficient of drag. In the same way as the cl , the cd is dependent of the shape and angle of attack of the wing. The drag force has a counteracting effect on the available traction force which propels the vehicle forward. By taking the addition of the theoretical drag into account, and knowing the efficiency of the engine, it is possible to estimate how much extra fuel the car would consume with wings.

Figure 1. The CFS12 without wings

THEORETICAL EVALUATION As mentioned earlier wings increase race car performance by providing “massless” load to the tyres. The wings will obviously add weight to the vehicle and the performance gain must outweigh the drawbacks of this extra weight and the addition of drag that wings also cause. How much downforce a wing produces can be described by the following equation;

(2) where L is the lift or downforce, ρ is the density of the medium in which the wing travels, cl is the coefficient of lift, Aw is the wing area and v is the wing speed relative to the medium it passes through. The coefficient of lift depends on the shape and angle of attack of the wing.

It can be seen in Figure 2 that wings have an effect on performance even with the relatively low speeds (the mean velocity of the CFS11 was approximately 56 km/h) of a FSAE car. Apart from the longitudinal acceleration, which unsurprisingly is affected negatively, wings seem to increase the accelerations. Especially the longitudinal deceleration has increased, i.e. the driver will be able to brake harder and thus later with wings. The theoretical increase in fuel consumptions due to the wings was calculated to 0.6 litres during an endurance run. This would have resulted in a reduction of 17 points (out of 1000 possible) for CFS11 in the Formula Student (FSUK) competition of 2011.

As mentioned earlier equation (1) describes the amount of lateral force the tyres can provide. The tyre's coefficient of friction is not constant and will decrease as the tyre load increases. This suggests that the available lateral force will decrease as the vertical force increase. The overall increase in lateral force is however larger than the decrease in friction coefficient [4]. The addition of the vertical aerodynamic force, L, to equation (2) gives total vertical force;

(3) By adding the theoretical addition of aerodynamic load to the logged data from the CFS11 it is possible to investigate how wings (or any downforce generating devises) affect lateral and longitudinal accelerations. Figure 2 shows a gg diagram, which plots lateral acceleration vs. longitudinal acceleration, for the CFS11 with and without the addition of theoretical wings. The logged data used is from the endurance event during the 2011 Formula SAE Italy competition. The wings

Figure 2. The effect of theoretical wings on a CFS11 gg diagram

WING THEORY There are a number of ways to alter the amount of downforce a wing can produce. Equation (2) shows, from a design point of view, that the size or area of the wing is influential as well as the coefficient of lift, which depends on the cross section shape, or the aerofoil, of the wing. The area of the wing is


determined by the width or span of the wing and the depth or chord, see Figure 3.

Figure 3. Explanation of wing terminology

The maximum span of the wing is determined in the FSAE regulations as is the chord in effect since the rules regulates how far ahead of the vehicle aerodynamic devises can protrude. To determine the aerofoils of the front and rear wing it is first necessary to know the desired downforce distribution or where the centre of pressure (CoP) should be. The CoP could be placed some distance behind the CoG of the car. This would have the effect that the vehicle becomes more under steered as the speed increases, as the relative load on the rear increses. This allows the car to over steer more in slow corners and thus turn in quicker but be more stable in high speed corners. With reference to the CFS12, the decision was made to place the CoP in the CoG and make the wings adjustable. This allows for the CoP to also be adjustable and a favourable position can be determined during on-track testing. Once the total amount of desired downforce has been determined along with the position of the CoP the downforce distribution can be calculated using a free body diagram, see Figure 4.

Figure 5. Centreline cross section showing pressure distribution

As the drag of the wings depends on the wings size and shape which in turn determine the downforce, this makes it difficult to decide the downforce distribution without investigating different wing concept's downforce to drag ratio. As a result of this, it is an iterative process to determine the downforce distribution. As the maximum size of the wings is determined by the rules it is easiest to look to the coefficient of lift to acquire the desired amount of downforce. There are various systems to describe the aerofoil of a wing, e.g. the NACA 4-digit series. The different numbers describe how much camber the wing has and its positions as well as the wings maximum thickness and its position [5]. By iteratively testing wings with different aerofoils and thus different downforce to drag ratios it is possible to determine suitable aerofoils to meet the required pressure distribution of the car. If a highly cambered wing is not enough to produce the required downforce, or results in flow separation, a multielement wing can be used. The most usual application on race cars is the use of flaps, which are smaller wings placed behind and above the main plane, see Figure 6.

Figure 4. Generic free body diagram (of CFS11)

The green arrows represent downforce and the red arrows represent drag. The position of the overall downforce generated by the underbody was approximated to roughly where the diffuser starts. This can be seen in Figure 5, which shows the pressure distribution of the cross section of the car along its centre line, as the low pressure region just below the engine in the lower left corner of the picture.

Figure 6. Wing main plane with one flap

This will increase the wing area but will also increase the effective camber without causing flow separation. One of the key parameters to consider when designing a multi-element wing is the size of the gap between the flap and the main wing. Experiments have shown that a vertical gap of 3.8 per


cent of the chord and longitudinal overlap of 5.2 per cent of the chord is suitable [6].

Table 1. Fluent settings

An additional method to improve the wing performance is the use of endplates. An endplate is a plate mounted vertically at the end of the wing (see e.g. Figure 11 and Figure 12). The implementation of endplates can potentially increase downforce and reduce drag. The general shape of a wing produces a pressure difference between the upper and the lower surfaces, which is also its purpose. At the side edges of the wing this pressure difference results in air flowing from the high pressure area to the low pressure area. This in itself decreases the effectiveness of the entire wing but also creates vortices trailing off from the wings. This results in an increase in induced drag [6]. Adding endplates to the wing will reduce the amount of air moving from the high pressure region and in general the larger the endplates the better they will work [7].

ANALYSIS To analyse different aerofoils for the front and rear wing and how they affected the overall pressure distribution CFD was utilized. Firstly, a computer aided design (CAD) model was created using CATIA V5 (Dassault Systems). ANSA (BetaCAE) was used to prepare the CAD model for simulation and to create the body surface mesh. Sharc Harpoon was used to create the volume mesh surrounding the car model, in effect a virtual wind tunnel. The dimensions of the wind tunnel was set to three car lengths in front of the car, eight car lengths behind the car, five and a half car lengths above and six car lengths beside the car. In order to decrease the simulation time and the required computational power it was decided to run half car simulations which can be mirrored afterwards to simulate a full body simulation, which is shown in Figure 7. It was decided that the right side should be used since this was the side with the engine radiator. As mentioned in the vehicle data section the front wing design has a significant impact on the air flow to the radiator. For the half car simulations between 11 and 14 million cells were used for the volume mesh.

The reason for choosing 15.56 m/s as the free flow velocity is that this is the approximated average speed of the CFS11 (56 km/h) and this was also assumed to be the average speed of the CFS12. The turbulence model used, the realizable k-epsilon model, is a time averaged (Reynolds Average Navier-Stoke) model using two extra transport equations, the k-equation and the epsilon-equation, in order to represent the turbulent properties of the flow. This is a suitable model when simulating turbulent flows and is relatively quick to solve. It was also used during the design of the CFS11 which makes comparisons between the two cars better. In order to achieve a good prediction of lift and drag forces it is important to set the ground plane as a moving wall and the wheels as rotating walls. This will more accurately simulate real driving conditions, comparable to the use of a moving ground system in physical wind tunnels.

The decision to run only half car simulations makes it impossible to simulate the behaviour of the vehicle during yawed situation. It was however decided that the increase in computation time would restrict the design process too much. To run the actual flow simulations Fluent (Ansys) was used. The properties that were investigated and which governed the design decisions were mass flow through the radiator, drag and lift forces. Important settings can be found in Table 1. Figure 7. Half car simulation


A fourth software, Fieldview (Intelligent Light) was used to visualize and analyse the CFD simulations.

CASE STUDY An open wheel race car represents a complex geometry and the half car simulations take between 12 and 40 hours per simulations with the resources available for the CFS project. As a means to reduce the simulation time and evaluate more concepts it was decided to run separate front wing and rear wing simulations. This is not optimal since the entire car influences the flow and especially the rear wing is highly affected by for example the roll hoop, the drivers helmet and the plenum which is situated just behind the drivers head. It makes it possible however, to distinguish between promising concepts and less promising ones. The front wing simulations were done using the same half body method as for the car and also featured the nosecone and the front wheel since this affects the performance of the front wing. The rear wing was simulated in a free stream flow since it is difficult to simulate the effect of the rest of the car without running a full car simulation. This method made it possible to reduce the number of cells in the volume mesh which in turn made it possible to use less powerful computers and still reduce the simulation time significantly. The desired amount of overall downforce was set to 500 N at 56 km/h and the design target for the diffuser was set to 30 N based on data from the CFS11.

of approximately ten degrees. The outer sections blend into a more neutral middle section with four per cent camber and an angle of attack of zero degrees, see Figure 10. The flaps have the same aerofoil as the outer sections, but a smaller chord. The influence of ride height has a significant effect on the aerodynamics and in particular the performance of the diffuser and the front wing. One example of this can be seen in Figure 5, which shows the significant low pressure region under the front wing as a result of ground effect.

Figure 8. Front wing concept with flaps spanning from endplate to endplate

Figure 9. Front wing concept with shortened flaps

Front Wing Several concepts were evaluated for the front wing design. Early simulations showed that the front wing should account for approximately 175 N of downforce and 30 N of drag to satisfy the required pressure distribution. It was also of vital importance that the front wing affects the airflow in such a way that a sufficient mass flow of air moves through the radiator. The duct inlet for the radiator was placed near the ground just behind the front suspension arms on the right side of the car. It was determined early in the design phase that a single wing would not provide enough downforce and a multi-element design was instead considered. After further simulations it became clear that a design with two flaps spanning from endplate to endplate, shown in Figure 8, would provide sufficient downforce but disturbe the flow to the radiator. The nosecone is not in Figure 8, but would be in the middle splitting the flaps in two. A design where the flaps were shortened to enable sufficient airflow to the radiator had the expected effect, but did not provide the required downforce, Figure 9. As a result, a more complex multi-section (lateral wise) wing was designed to ensure sufficient downforce and air flow to the radiator. The outer sections, with shortened flaps, consist of an aerofoil with 15 per cent camber and an angle of attack

Figure 10. Final front wing concept

Rear Wing As with the front wing, several concepts were evaluated for the rear wing. To maintain the required pressure distribution it was concluded with initial simulations that a rear wing providing approximately 295 N of downforce and 110 N of drag was required. The main challenge during the design of the rear wing was to understand how the downforce and drag values differed between the free stream wing simulations and the half car simulations. A single element wing was quickly ruled out and several alternative concepts of multi-element wings were evaluated, mainly two-element concepts (Figure 11) and three-element concepts (Figure 12). The effect of different sizes of endplates was also investigated. After several half car simulations a three-element design was chosen with a main wing aerofoil with ten per cent of camber and an angle of attack of ten degrees. The flaps have 15 per


cent of camber. Both the front and the rear wing have adjustable flaps.

Figure 11. Two-element rear wing concept with large endplates

Figure 12. Three-element rear wing concept with small endplates

accurately simulate separation, or because there is no separation. This potential problem with the rear wing leading edge was unfortunately not discovered until manufacturing of the wings had begun. In order to investigate whether or not the wings suffered from flow separation in reality flow-visualization tuft of yarn was attached to the underside of the wings during on-track testing and filmed using a video camera, see Figure 17 and Figure 18. The yarn tufts follow the airflow, meaning that an attached flow should keep the yarn to the surface of the wing. Flow separation will however result in turbulence which will cause the yarn to flutter in a seemingly random fashion.

Figure 13. Pressure distribution behind rear wing

As stated, the performance of the rear wing is highly influenced by the rest of the car and it is important to investigate this influence. CFD simulations require post processing and interpretation of the results. For example, the proximity between the plenum and the rear wing greatly affects the performance of the rear wing which can be seen in Figure 5 and Figure 13. Figure 5 shows how the plenum affects the low pressure under the wing and Figure 13 reveals how the pressure distribution under the rear wing changes when moving the entire wing back ten centimetres. It shows the car from behind, with the right hand side of the figure showing the wing moved back (the wing mounts are also featured). The CFS12 with its full aerodynamic package can be seen in Figure 15. It is also important to realize that CFD simulations are only an approximation of the reality and unless the volume mesh cell size is very fine the results can vary greatly from real life. Even with a fine mesh, CFD simulations should not be considered to reveal the absolute truth. Figure 14 shows the leading edge of the rear wing from a half car simulation. It can be seen that the leading edge is actually situated a few centimetres up from the ideal position in the very front of the wing. This is probably caused by the fact that the air flowing over the car hits the rear wing with an angle and this forces the air to move against the free stream direction in order to reach the underside of the wing. This could result in flow separation on the underside but the post-processing showed no signs of this. This might be because of the relatively coarse volume mesh, which could lead to a failure in

Figure 14. Leading edge of rear wing

Figure 15. The CFS12 with wings

RESULTS The final design was firstly evaluated using CFD and later during pre-competition testing where lateral and longitudinal


accelerations were logged and potential flow separation was investigated using flow-visualization tufts.

Computational Fluid Dynamics The final design of the front wing was presented in “CASE STUDY” under “Front Wing”. The initial simulation, with only the front wing, the nose cone and the front wheel, showed that the front wing alone would produce approximately 184 N of downforce and 32 N of drag. This is to be compared to the design target of 175 N of downforce and 30 N of drag. When using this front wing in the half car simulation the values changed to 172 N of downforce and 30 N of drag. In the free stream simulation the rear wing produced approximately 442 N of downforce and 142 N of drag, compared to the targets of 295 N of downforce and 110 N of drag. The reason for the big difference, especially in terms of downforce, is that earlier simulations showed a loss of approximately 30-40 per cent from free steam simulation to half car simulation. The half car simulations showed values of 272 N of downforce and 108 N of drag. This, together with the front wing and the rest of the vehicle, gave a total amount of downforce of 477 N and 253 N of drag. Even though the rear wing did not meet the design targets it was assumed that it was sufficient and that this could be compensated for by the adjustable flaps.

Pre-Competition Testing Due to the realisation that the angle of attack of the rear wing might result in flow separation it was decided that the angle of attack should be lowered. Manufacturing of the wings had already begun and due to resource restrictions further 3D simulations could not be used. This made large design changes impossible and simpler 2D simulations resulted in the decision to lower the angle of attack by seven and a half degrees. In an attempt to exploit the phenomenon of ground effect on the front wing, it was initially mounted close to the ground, approximately 35 millimetres. After tuning the suspension during testing, which resulted in a lower ride height, this proved to be too low and the wing contacted with the ground during braking and roll. To avoid this the front wing was mounted higher, eventually 80 millimetres higher than intended. The resulting loss of downforce due to ground effect significantly altered the CoP and the car began to understeer. To solve this problem the angle of attack was increased by approximately seven degrees. It was estimated that the modifications to both the front and rear wing reduced the overall downforce but a suitable CoP could be achieved. This received positive feedback from the drivers. It was initially intended to investigate the amount of downforce by using potentiometers mounted to the dampers of the car. Due to technical difficulties this was unfortunately never realised.

The effect of the aerodynamic package could however be measured in other ways. The on-board sensors logging lateral and longitudinal acceleration were used to construct gg diagrams showing the effect of the wings. Figure 16 shows a gg diagram from the first test with the modified wings. The car was first driven without wings around an approximately 800 metre track designed to resemble an FSAE endurance track. The wings were later mounted to the car and the same driver drove the around the track.

Figure 16. The effect of wings on the CFS12 during precompetition testing

It can be seen that the effect of wings in the testing gg diagram is not as profound as in the theoretical gg diagram. Surprisingly the longitudinal acceleration seems unaffected. The lateral accelerations show little change but the longitudinal deceleration increased. During this first test with the modified wings a two second difference was recorded over one lap, in favour of the wings. During on-track endurance simulations, with and without wings, it was shown that the wings increased the fuel consumption by approximately 0.6 litres. It should be added that the test described above was the only one performed when the car was driven with and without wings as a way of evaluation. Once it had been established that the lap times had decreased the decision was made to utilize the wings. As mentioned, flow-visualization tufts was used to evaluate eventual flow separation, Figure 17 and Figure 18. This was considered especially important after the modification of the wings since both the wings had been altered compared to the CFD simulations. The left picture in both figures shows the car in straight line acceleration while the right picture shows low speed cornering, giving some justice to the claim that wings do not work in low speeds.


No main plane separation could be detected on either of the wings, but high angle of attacks on the upper flap resulted in some separation on both wings. According to the drivers, more downforce could be produced by lowering the angle of attack of these upper flaps, which was also demonstrated by the tufts.

consumption, which accounted for approximately half of the lost points during the FSUK competition. To be able to design an aerodynamic package in the short time available, in FSAE a new car is usually designed every year, it is in practice necessary to use CFD. Since there are many parameters that must be considered when working to achieve the required design targets in terms of downforce, drag, CoP and cooling air flow, it is vital to be able to analyse different concept before the car is manufactured. It should again be noted that the investigation only included straight line performance and no yawed situations were simulated, which obviously limits the conclusions that can be drawn. Even if the simulations have relatively low resolution, in terms of number and size of volume mesh cells, CFD is still a useful tool in the design process. It is however important to realise that CFD is an approximated representation of reality and on-track validation is necessary to investigate the actual performance of the wings. This can be achieved using on board sensors or flow-visualization techniques, but in the end it is the increase in overall performance and the drivers' ability to reduce lap times that matters.

REFERENCES Figure 17. Flow-visualization tufts on rear wing

1. Barnard, R. H., “Road Vehicle Aerodynamic Design”, MechAero Publishing, Hertfordshire, ISBN 9 780954 073473, 2009. 2. Racecar Engineering, “Wings and things”, http:// www.racecar-engineering.com/blogs/wings-and-things/, July. 2011. 3. 2012 Formula SAE® Rules, SAE International, Warrendale, PA, 2011. 4. Milliken, W. and Milliken, D., “Race Car Vehicle Dynamics”, Society of Automotive Engineers, Inc., Warrendale, PA, ISBN 978-1-56091-526-3, 1994. 5. Abbott, I. H. and von Doenhoff, A. E., “Theory of Wing Sections”, Dover Publications, New York, ISBN-13: 978-0-486-60586-9, 1958. 6. McBeat, S., “Competition Car Aerodynamics”, Haynes Publishing, Sparkford, ISBN 1 84425 230 2, 2006. 7. Katz, J., “Race Car Aerodynamics”, Robert Bentley, Cambridge, ISBN 0-8376-0142-8, 1995

Figure 18. Flow-visualization tufts on front wing

SUMMARY/CONCLUSIONS It has been seen that wings can have a positive effect on the overall vehicle performance of a FSAE formula racer, even with its relatively low speed range. The CFS12 was a highly successful car, being the overall winner of the FSUK competition of 2012 and finishing third overall in the FS Germany Combustion competition of 2012. The major drawback caused by the added drag was an increase in fuel

CONTACT INFORMATION Sven Rehnberg Chalmers University of Technology Applied Mechanics SE-412 96 Gothenburg SWEDEN [email protected]


ACKNOWLEDGMENTS The authors of this paper would like to sincerely thank the then Ph.D. (now Dr.) David Söderblom for all his help, especially with CFD and analysis. The authors would also like to thank Volvo Car Company for all its help during manufacturing of the wings and for providing test tracks.

DEFINITIONS/ABBREVIATIONS CAD - Computer Aided Design CFD - Computational Fluid Dynamics CFS - Chalmers Formula Student CoG - Centre of Gravity CoP - Centre of Pressure FSAE - Formula Society of Engineering FSUK - Formula Student UK NACA - National Advisory Committee for Aeronautics

Aw - Wing area [m2] C d - Coefficient of drag [-] C l - Coefficient of lift [-] D - Drag [N] F y - Lateral force [N] F z - Vertical force [N] L - Lift [N] v - Velocity [m/s] µ - Coefficient of friction [-] ρ - Density [kg/m3]

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The Design Process of an Aerodynamic Package for an FSae Car

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