The wind tunnel (WT) tests are carefully scheduled and organized, because the cost of this tool is very high. Hence, a basic flowchart of this tool is composed by Preparation, Testing and Output. Usually, in just one session, several runs are made, each of them using as many configurations as possible. When a run is finished, its data is immediately analyzed to decide if this represents an improvement relative to the baseline configuration. This article proposes an overview about the WT data analysis process.

Analysis steps

The data analysis has the following steps:

• Post-processing;
• Data analysis;
• Decision.

Inside these there are sub-steps as post-processing, post-processing softwares, diagnostics, aerodynamics analysis and decision-making phase.

Post-processing

The post-processing is a consistent and quick data manipulation according to the test requirements. In some cases there are softwares or optimized tools just for post-processing, these help to manipulate data and make them ready for analysis. Hence, the post-process has three requirements, readiness, completeness and coherence, basically these are confused with the wind tunnel requirements. The readiness is the capability to make the data available as soon the test had finished. In addition, readiness is also the capability to follow the data in live-mode. Completeness is a proper data reconditioning, in other words, take this one and average, weight, re-balance and re-drag and apply these data into graphic tools, which can be 2D and 3D plots. The coherence is the capability of the software to sort the data as requested, it is usually done by time and target of the WT test.

Software layout

Usually the softwares used in Motorsports wind tunnels have a general layout as the one illustrated by Figure 1. The windows are usually configured according to the example in Figure 1. The run can be grouped as sort of folders, as Windows one, thus the database is divided job by job. Hence, it is possible to take from a run list for which option will be set a job and the relative datum. This last one is the reference run, the baseline wind tunnel model (WTM) configuration, which will be used to perform the reference analysis. The reconditioned data are the averages, the baseline and all other jobs and some aero maps, that give the possibility to judge the car behavior.

As seen in Figure 2, with the aerodynamic coefficients it is possible to build aero maps that correlates these with the ride heights (RH). The 2D plots relate RH with the aerodynamic coefficients, while 3D aero maps are more related to surfaces and the flow in which these ones are immersed. The analysis moves from general to a particular one. For instance, it starts with the average data, then it performs the comparison between the data. After that there is the stability map, which is a plot of the variation for the aerodynamic coefficient relative to the front and rear ride height, FRH and RRH, respectively. The radiator map illustrates the mass flow over the surface, while the underwing/bodywork maps are used when there are pressure taps on the wind tunnel model (WTM), thus it is possible to visualize the pressure along important surfaces as the diffuser.

Data analysis

The process of data analysis is composed of the diagnostic phase, the aerodynamic analysis and the decision. Each run is divided into two phases. The first phase is the acquisition of forces, model positions and parameters that the positions are known. The second phase is the acquisition of parameters which will not achieve any aerodynamic effect.

Diagnostic phase

In order to perform the analysis avoiding the loss of the reliability of each run, both phases should be accounted for. For each of these, the values of WTM, rather than the facility ones, has to be taken into account. These are typical examples of the analysis performed regarding the model position in both phases, tare and wind on.

Tare phase

In the tare phase it is analyzed as the main aerodynamic coefficients C_XS and C_ZS. In addition, it is in this phase that the bridging phenomena occurs. This is an unwanted connection between the model and wind tunnel environments that part of the forces pass through to one and another. There are also resistances that come from the wheels, which can affect the reliability of the measure since a higher resistance results in an effect called drift. Therefore, in the tare phase it is performed readings of the model positioning, the forces in both x and z directions and the measurements of the wheel rolling drag.

Wind-on phase

In high level WTM there are pneumatic tires, thus the pressure has an important role since it controls the tire contact patch. In addition there are also the effects of pressure on the rolling resistance. For this reason it is important to keep under control the pressure and the temperature of the inflated air. If the position of WTM is lost for some reason, the software can have an automatic replica of the configuration, thus the gain in time to move the control for user-defined is reduced. Therefore, the wind-on phase deals with the reading of the model positioning, the tire pressure and temperature and the wind tunnel flow characteristics.

Bridging phenomena

There are two common examples of the bridging phenomena. The first one occurred in the tare phase. In this one it is possible to observe that at some point, the whole model goes from zero to a very negative value. This suggests that at some point the underfloor of WTM is touching the surface. The shift between the signals identifies the problem.

In case of a high level WTM, the wind-on phase can exhibit drift. This occurs due to the tire pressure drop and can be observed by the ride height (RH) difference between the wheels (Figure 3). From the diagnostic point of view, there are specific controls that are performed to avoid effects like bridging and drift.

Data analysis

In the analysis process the focus is the deltas respective to the baseline. These are items analyzed one by one. First, there are the aerodynamic coefficients, which are composed of the averaged coefficients, the stability and the sensitivity plot. The stability plot is the graphical visualization of the aerodynamic coefficient variation respective to RH. The sensitivity plot is the graphical visualization of the aerodynamic parameters respective to yaw and roll. Usually the procedure defines that stability should be firstly verified, then the sensitivity plot is checked.

The aerodynamic coefficients are based on the longitudinal and vertical forces acting on the car, thus C_ZS and C_XS, which are based in the reference frontal area of the car, are given in m². The non-dimensional parameters are the efficiency Eff and the front balance F_bal. The variation of the reference cross-section results in different RH and its shape. In addition, it is possible to split those coefficients between bodywork and wheels, which allow the measurement of the C_XS due to the wheels and the bodywork separately. In a similar manner it is possible to have cells on uprights and wheels to have a similar evaluation for C_Z between body and wheels given the fact that, since these kinds of cells are mounted on the upright, they measure part of the vertical load of the wheel. For example, the vertical load produced on the aero devices that are on the inner side of the wing. The cells can not measure the total lift of the wing, only the diffused load. For this reason, there is no full measure of the load on the wheels, they require additional instrumentation and this does not often use the standard instrumentation. Hence, the total downforce C_ZTS is used to measure the value of the entire car.

Main data subsets

Once the aerodynamics coefficients and the aero maps are implemented, these are histograms of RH and the combination of the five parameters respective to RH. Although Figure 5 illustrates a history of 10 RH configurations, a real aero map has about 30 – 40 configurations. If the deltas between the baseline and the option are performed, the first output would be a table with all deltas. However, the analysis in this form of the deltas is not an easy and fast approach, because it is just a big sequence of gains and losses. Hence, one point is:

1 pt = 0.01 C_ZS

1 pt = 0.001 C_XS

The colors at Figure 5 are used to highlight where there is a gain or a loss. For instance, a negative drag represents a gain, thus it is exhibited in blue words. This is also valid for C_ZS, because the reference system is positive upwards. Hence, the ride height 1 from delta table (Figure 5) can be read as a gain of 0.3 points, a loss of 0.6 pt and a loss of 1.2 pt for C_XS, C_ZFS and C_ZRS, respectively. It is possible to notice that C_ZS, Eff and F_bal varied between – 1.9 pt, – 0.7 pt and – 1 pt, respectively. A negative ΔF_bal means that part of the balance was moved backwards. Since for RH there is a gain and a loss, this is just for one RH. When all of them are put together, it is difficult to analyze all that data. 

Hence, it is defined some subsets which are simplified. First, it is performed an average, took the deltas of all those RH, averaged and weighted in order to have a big table of delta reduced to one row (Figure 6), which is not anymore related to a RH, but just to the averaged of all of them inside the aero map.

Structured aeromap

Another procedure can be adopted if the aero map is a structured one. This kind of aero map is characterized by the RH information drawn in a such way that it is possible to isolate some groups of RH, that allows to analyze the aerodynamic parameters one by one with respect to the variation of position parameters of the car. For instance, using the structured aero map, it is possible to take the subset from the aero map and plot the stability graph. The group of RH with steer and yaw fixed and just front ride height FRH and the rear ride height RRH free to vary. This allows to trace the stability map for each aerodynamic coefficient. Another procedure is to keep a group of RH, which one by one roll, steer and yaw are only positioning parameters that are changing, to draw the sensitivity graph. It is important to understand that there is no value which is valid for each wind tunnel, but roughly, 1 pt in C_ZS and 2 – 3 in C_XS could be a reasonable stability range to be considered.

Repeatability

Hence these deltas on the sum of the ride height are close to the repeatability. The experimental data is applied for each RH to obtain the result, which is the delta. Hence, the average is performed. For sure some of those deltas can be in the range of the repeatability. It is up to the aerodynamicist to judge the result with respect to the repeatability grade. Figure 5 illustrates the delta between two options once the average is done. At this stage the data is simplified a lot, but still is not suitable for the analysis. It is possible to notice that there is a small delta in C_XS, a lose of C_ZFS (⋍ 5 pt) and a gain of 2 pt of C_ZRS. There is an effect on F_bal and Eff. The first is usually highlighted, because this is the first item to be analyzed since it is the most important for the car performance.

Re-balance

The re-balance target for a given car is quite a strong target of the project. Regarding a car to install an aero device, which is called option, observing its delta it is not possible to define if the modification is an improvement or not. Actually, even driving a car with both configurations, it is only possible to infer some comments about the front balance. The driver is not able to comment about the drag or downforce. The first step to re-configure the condition of this data is, the re-balance. For this is required a tuning parameter, usually the wing, and its polar curves, to perform a process that the results are compared for the same balance. It is not advisable to compare values with a balanced delta between them. The second step is the re-drag. If there is a second adjustable parameter, for instance, on the rear wing, it is possible to perform the re-drag. This means that for the same drag values C_ZS is varying. Therefore the first step is the variation of the aerodynamic coefficients without F_bal variation, which is the re-balance, while the second step is the variation of the aerodynamic parameters without variation on drag.

Iso-laptime slope

The re-balance usually is the first step, its adjustable parameters are the angle of the front and the rear wings. Polar curves are used, because they provide the ratio between C_XS and C_ZS with F_bal, all of them are functions of the wing angle. These data can be available from previous wind tunnel sections, CFD simulations, or at the beginning of the development history of the wind tunnel model of the car, the data produced can be used as base for the data reconditioning. It is not required to adjust the wings of WTM physically. Actually, in the reconditioning of the data it is just required the check if the options, the geometries and the runs are at the same target value of F_bal. Hence, balance in this case is not variable anymore.

Once this kind of reconditioning is performed, the C_ZS and C_XS are changed. These parameters result in ΔC_ZS and ΔC_XS, since there are several options. The ratio between ΔC_ZS and ΔC_XS is called re-balanced marginal efficiency Eff*. This is called re-balanced, because it is a ratio between ΔC_ZS and ΔC_XS, but this is not the efficiency of the car. This parameter is composed by deltas after the process, this is indicated as the efficiency line, different from the efficiency presented for each option and the baseline.

For comparison purposes there is another efficiency, Eff*, which is a predetermined project constraint. This is defined as the slope between C_ZS and C_XS that comes from the lap time simulator or track tests. In other words, if Eff* is plotted, this divides the graph in two regions (Figure 9). The region in light blue is where there are improvements on the performance, while the white area is where the performance is reduced. If the ratio ΔC_ZS/ΔC_XS is exactly equal to this slope, but about the upper right region, this means that the car is producing more drag and downforce, thus faster on corners, but slower on straights. The lap time itself depends on the kind of circuit. If the car moves away from the line, there are two easy cases. First, the car could be at the bottom left region, which results in low downforce, but with low drag. The second case depends of the slope of Eff*, which can be in a region of high downforce, but high drag or in a region where both quantities are low. The analysis compares the variation of C_XS and C_ZS, but with one parameter fixed, usually F_bal. The ratio between them is project constraint, the iso-laptime slope. This is the way to analyze the averaged data, re-balancing but not re-dragging. Hence, for projects which, for some reasons, it is decided to perform only the re-balance, re-drag is not adopted as a target. In this process it is possible to accept an option as positive, in which drag is increased or reduced and the car can move its optimal configuration job by job. An important comment about the influence of the track in defining this slope, the marginal efficiency Eff*, is that there are different values depending on the track.

For instance, a fast track like Monza usually exhibits a high Eff*, because it is important to have a lower drag. In tracks like Barcelona, which requires a high downforce, this number tends to be smaller. The value of Monza usually ranges between 3 and 6, for open-wheels race cars. This means that, to compensate for 1 point in C_XS, 6 points in C_ZS are requested. The same evaluation made for Barcelona can result in 1 point for C_XS by 2-2.5 points for C_ZS. Hence, this basically changes the slope of Eff* line. The key point is that the development takes the information about all tracks to build slope lines and these drive the choices during the development. In the case of Monza, it will keep a lot of options that in another track will not be suitable. It is possible to work with a sort of an average parameters for a given car, maybe considering a high downforce track since these are the most common.

For example, F1 and some other open-wheel cars like F3, for specific conditions as Monza, it is required a specific development in which it is defined with different aero configurations that result in the adoption of a different lap time slope. This is the case when it is considered all the constraints (Eff_n* , for n ∈ ℝ) together, because the blue area (Figure 11) becomes more and more reduced. This means less opportunity for improvements.

Supposing a target of Eff* = – 3.5 and the deltas illustrated at Figure 12. The option is re-balanced by the front wing polar, then the new data is labeled. It is possible to notice that Eff* is equal to – 2.566 and the slope target is – 3.5. Once the re-balanced C_XS is lower, C_ZS is also lower, this configuration will end up inside the light blue area. Hence, this option represents an improvement.

Re-drag

The step after would be the re-drag if the project has quite strong drag constraints. This means that, since the knowledge about the car design is known, all the performance parameters are thought in order to keep C_XS under control. It is something possible, but specific for projects where there is a strong aesthetic car design. It uses a second adjustable parameter. If the front wing is more convenient to adjust F_bal, the rear wing angle is used to control drag, because it has a polar which moves more C_XS than the front wing polar.

Iso-balance curve

In this way, it is possible to build the iso-balance curve. This is a characteristic curve of the car that can be obtained by changing the front wing angle α₁ and the rear wing angle α₂.

However, the combination of these two are always at the same F_bal, but varying C_XS and C_ZS (Figure 13). In addition, supposing that this curve is bilinear and that the re-balance was already performed, it is used the projection of the iso-balance curve to keep the values of the aerodynamics data of the runs which are being analyzed to bring both values (C_XS and C_ZS) to the same C_XS, 0.85 for this case (Figure 13). Hence, the evaluation of the configuration is easier to perform since C_XS and F_bal are fixed, the only variable parameter is C_ZS. Hence, the case illustrated in Figure 13, the option is the best configuration, because it produces a higher downforce for the same drag and front balance.

Iso-laptime slope and Iso-balance differences

It is important to notice that the method that performs re-balance compared to an iso-lap time one, can exhibit different results when compared with re-balance and re-drag. In one case it is possible to identify that the option is better than the baseline, but if the iso-laptime slope is different from the iso-balance slope, as in Figure 13, the option point is out of the improvement region. If the iso-balance curve is doing the re-drag, it is possible to visualize that the option in terms of C_ZS, after re-drag, is higher. The difference is the fact that once it is applied to the re-drag process, it is assumed that comparing the two options, which is an artificial comparison, the balance should be compensated, and the rear wing is used to compensate for drag. This adjustment on the rear wing is what moves the slope. Actually, the rear wing is the game change between the two, in this case. Hence, if the rear wing is not compensated, the car will be slower since too much downforce comes at the cost of too much drag. This is valid for the iso-lap time method. In the case of the iso-balance method, it is possible to force in the same value adjusting also the rear wing. In other words, fixing F_bal and C_XS, this second adjustment can change the judgment that is possible to do. There is no physical reason for that, the first method allows more freedom, drag can move and is compared to the lap time. In the second method there is a second constraint that behaves as the slope.

References

• This article was based in the lecture notes written by the author during the Industrial Aerodynamic lectueres attended at Dallara Accademy.