When evaluating a race car aerodynamics it is defined some parameters to characterize its aerodynamics according to the track and race conditions. It is created an analytical relationship between these parameters, the typical relationship is called polar curves. There are two types of polar curves, the wing polar and the cooling polar. The first is the most commonly used during aero development. It is defined by the variation of the attack angle of the wings. It is important to mention that open wheels (OW) and closed wheels (CW) race cars have different aerodynamic devices. Open wheels race cars has wings at front and rear, while the second has only one wing, at the rear part of the car. These are used to optimize the car setup. The race teams have those polar for the wings and use this information to define a setup for a track or specific condition. These are the front wing and rear wing polar. In addition, it is possible to use the polar curves during the aerodynamics development in order to perform data recognition. This is a process that recognizes the output data from a wind tunnel test, so that it is able to compare different wind tunnel runs.

For instance, to compare different wing configurations by fixing one parameter, front balance (F_bal) or drag (C_X∙S) as examples, it is possible to define which configuration is better. Figure 1 indicates an example which the front balance is fixed. The red line indicates the polar obtained just changing the wing angle, option 1 and option 2 are data measured by wind tunnel tests. In addition, by fixing the front balance as a target of 41, it is possible to choose the best solution. In case of cooling polar, this is based in the mass flow rate through cooling ducts. Hence, some blanks are designed, the mass flow rate is imposed, thus it is observed how these blanks impacts on cooling and also on aerodynamics coefficients, mainly drag (C_X∙S).

Wing polar curve

An important variation of the wing polar is the three dimensional curve. This bring together the front balance (F_bal), the drag and the downforce in one graph. From this it is possible to obtain two curves, one respective to F_bal and the other respective to C_X∙S. However, it is important to understand that all parameters are related to C_X∙S, this is a typical polar used in the aero development. Considering the wing polar evaluation, open and closed wheels race cars differ in the amount of wings. Usually, CW race cars have just one wing, at the rear of the car, while OW one has two wings. This results in different polar curves since the front wing disturbs the airflow for the rear one.

General case for open wheels race car

In case of a OW race car, the front wing is one of the first to be analyzed. An interesting point about the front wing is that adjustments are made on the wing flap. The already mentioned polar curves are used. As can be seen in Figure 2 and 3, increasing α of the front wing, the downforce increases at a very small cost of drag. In addition, the curve equation demonstrates that the efficiency of this front wing is very high. The efficiency is the amount of downforce by the amount of drag (Eff = C_ZS/C_XS) .

A high efficiency wing is characterized by the ratio between the downforce and the drag produced which produces the highest downforce with the smallest drag as possible. The equation suggests that, for one point of C_X∙S, the downforce increases about 5.6 points. In addition, changing α also change F_bal. As higher α, more the balance of the car goes towards the front axle, thus increasing F_bal.

The rear wing polar exhibits a different situation. Figure 4 and 5 illustrates that although the downforce increases with α, the efficiency is lower than that the front wing α. For one point of drag, the downforce is increased by 2 points. F_bal is also changed in a different regarding the front wing. In this case, a higher α transfer the balance to the rear axle. Hence, the front balance is reduced. Figure 2 and 5 illustrated how front and rear wings are used to setup the car.

These wings have very different polar curves mainly in terms of balance. The reason is, if there is one value of front balance which is the target, both front and rear wings can be used to achieve it. In other words, it is possible to increase the front wing α or decrease the rear wing α. For this reason, it is important to know F_bal target, the situation and the track layout. For instance, in a low downforce track, it is interesting to set the car to perform a lower drag in order to improve the maximum velocity. Hence, it is required to shift the balance to the front by reducing the rear wing α, because this one has a higher impact on drag. In this way, the balance is shifted to the front, while C_X∙S is reduced, thus improving the top speed of the car. Conversely, in wet conditions, it is advisable to work on the front wing α to increase the grip and F_bal at low cost of C_X∙S. In this way, the drivability of the car is improved. Therefore, the car balance due to the wings must be carefully adjusted since each wing acts over the axle which they are near to. Downforce always comes at some cost of drag, but the ratio is worst on the rear wing. This occurs, because the rear wing catch some wake from the front wing and wheels. Wings are adjusted by angle variation (α). This is made on the flap or on the entire wing. Usually, front wing have flaps, while the rear wing move entirely.

Figure 6 illustrates the correlation between F_bal, C_X∙S and α of each wing. These confirm that the front wing is less sensible to C_X∙S than the rear one, the slopes are 0.002 against 0.014, respectively.

Cooling polar curve

The cooling polar is important, because it has a significative impact on aero coefficients. It is measured the impact on them due to the variation of the radiator cross-flow. This is performed by the obstruction of these blanks, as seen in Figure 7. The test is performed and the new aero coefficients are calculated.

According to Figure 8, the effect is clear, increasing the blanks, in other words, the reduction of the airflow rate through the radiator, lower will be C_X∙S, higher the efficiency. However, it is important to understand that less airflow to the radiators, means an engine operating in a critical temperature. Therefore, the engineer must understand that a compromise between C_X∙S and engine durability should be very well stablished.

Louvers polar curves

Despite front and rear wings, there are other polar curves, from devices that have a significative impact on the vehicle aerodynamics. For instance, underwings, diffusers and the flat floor. However, a polar curve is defined by an adjustable parameter and its correlation with the aero coefficients. Since these are not adjustable, an aero device which is adjustable is the louvers (Figure 9). These are usually found in GT and old prototype cars. This device propose a connection between the front underwing and the external flow field.

When open, louvers create a suction effect that improves the vertical downforce. However, there are some costs due to the use of louvers. The first is C_X∙S, if the slots are closed, C_X∙S generated is reduced, but also C_Z∙S at the front axle. Hence, F_bal is also reduced. Another consequence of the louvers is the cooling, in some cars, the intercoolers are at the rear part of the car. The air that exit the louvers goes directly to the intercooler ducts. Therefore, louvers also requires the understanding from the engineer about the compromise between a good F_bal and the engine cooling.

References

• This article is based on the authors notes taken during the Industrial Aerodynamic lectures at Dallara Academy.