The fourth part of the math channels built for race car data analysis will approach the details of these. Although the math channel is relatively easy process, the detail identification require some case examples. This proposes some discussion about acceleration G, corner radius, gear and throttle acceptance. In addition it will be discussed what be extracted from these channels when gating those data.

Longitudinal, lateral and combined G

Figure £ illustrates a plot of the lateral acceleration, the throttle and the lateral G times the throttle signal. These are given by the black, the red and the gray lines, respectively. The Gy times the throttle is a math channel given by the logics seen at Figure 1. It defines that the if the throttle is above 70%, then the channel returns 1, if not it return 0. This is a logic channel. However, this channel can also be given in the analogic form. In this case, the math channel is defined according top the formulae seen at Figure £ and written below:

Gy∙Throttle = Gy∙IF((Throttle) > 70%; 1; 0) → Logic on/off

Gy∙Throttle = Gy∙(Throttle)/100% → Analogic

Instead of 0-1 values, this is a continuous values. Hence, it allows to spot the partial throttle activations. The difference between them is the amount of information that the analogical math channel is capable to provide. When the red and black lines match, it means that the car is at full throttle. Therefore, starting from two uncorrelated parameters, lateral G and throttle, it is possible to build a math channel that delivers Gy when the driver reaches full throttle. Another difference is that the logic channel is a bit subjective since it should set the threshold considering full throttle. Each corner has a peak of lateral G, then the next will have a different one. Hence, if it is plotted Gy at full throttle divided by the peak value of Gy, it is possible to notice how close to the limit the car is when at full throttle. A good car is able to reach 80-90 % of this ratio. Analyzing the dataset, it is possible to create references to predict this ratio. For instance, for a given speed or radius, that car should be able to perform a determined ratio.

ay(FT)/ay(peak) [%]ay(peak) [G]Radius [m]
751.850
702.6100
803.2150
Table 1

With a good database, some tables as Table 1 can be built in order to promise the data. Hence, creating a math channel as functions of time or distance. Since the database provides all data, it is possible to create a math channel which polynomial equation in function of radius. Hence, it is possible to have a prediction of this ratio. Usually, when the radius is higher, the ratio tends to be higher. The reason is due to the aero effects. However, in grip limited corners, this ratio can reach high values. This depends on the car balance and the driver skills. In addition, in tight low speed corners, the driver is able to apply full throttle easier, because he/she can manage the oversteer. However, in high speed corners this is not manageable. If the car has a high speed understeer, it is possible to spot it immediately. Since the peak of the lateral G is different at each corner, a math channel for the can be built. While the peak of Gy is different from Gy at full throttle, the channel returns zero. Hence, this channel returns zero before each corner. When the throttle is down, the modulus of steering is below threshold (user defined), that means a new corner. Then the lateral G at full throttle occurs and since the peak of the lateral G is known, the ratio can be calculated. This ratio is peculiar to a determined driver/car balance.

Corner radius

Figure 2 illustrates a plot of the turn radius, the modulus of the turn radius and the speed. The radius has a positive and negative sign, because it is determined by the lateral G one. Based on the radius, it is logged the speed and the lateral acceleration. For each corner, it is possible to save the value of the peak of Gy. Each corner has a different speed or different radius, thus it is possible to create the numerical term of the peak of the lateral acceleration versus radius. Hence, if the track has 10 corners, the amount of data generated will be 20 points. Then, it is possible to note the ratio between the lateral acceleration at the full throttle conduction and at the peak. This could be in function of the radius or at function of speed. After this, it is calculated the polynomial equation, which is the ratio at function of the radius. Once it is obtained this formula, every radius allows to predict this ratio. It is accepted that in some corners the values would be out of the prediction, this is part of the data analysis. With the dataset, it is possible to build a plot with the predicted values and compare then with the one which is being measured during outing. This allow to spot immeadiately situations where this ratio is below the expected without too much analysis. Actually, this is a process that transits between the analysis and synthesis. The first is performed when it is alarmed by the synthetic process. For instance, the under torque alerts that there is a possible detail issue. Hence, a synthetic channel that goes into detailed analysis. If the analyst stays only on the analysis mode, then the data analysis will take more time.

Gear

The x-y graph is a common way to plot speed versus engine revs. However, there is also the strip chart, which is useful for comparisons. Instead of plotting speed and revs separately, it is possible to build a graph with speed and gear channels and overlay them. For instance, Figure 3 illustrates a strip chart that plot the RPM overlaid by the gear signal and the same, but using the speed one. The choice of which one is best is subjective. The driver has no perception of the speed, the same can be inferred about the lateral acceleration. Actually, this last one is a kind of raw parameter in the point of view of the driver. Hence, the driver is not able to quantify those data. In the point of view of the driver, only the engine revs and the gears are quantified, because it is on the dashboard or he/she can remember them.

Gear math channels

Gear channel also allows the creation of some math channels together with throttle. This can be logic or analogical. These can be the ones seen in Figure 4. This channels allows to easily spot each gear that the car is at determined situation. For instance, which gear the car is when at full or partial throttle. The gear means when there is connection between the engine and the wheels.

Figure 4 illustrates a plot of the logic channel. As can be seen, the gear information only appear if the throttle is above 70%. The objective here is to show the gear when the car is at full throttle, but excluding the partial throttle situations. The selection of the percentage is subjective and according to the situation. Data analysis should be a clear tools and representations of the communications between the driver and the engineer.

Gating

Gating is a process to count events. For instance, if it is necessary to count the events respective to the lateral acceleration above 0.5 G. Hence, on straight and braking these will be considered non-events. A lap of 100s (1″40s) and sampling rate of 50 Hz generates 5000 events. The number of events above 0.5 G represent 30 % of the total events. Hence, there are 1500 events. Then the average of the lateral acceleration events should take into account. All the rest is zero, thus if the average accounts the 5000 events its value will be much lower. It is necessary to know the average of the lateral acceleration only for the valid events. These are based on the criteria established by the analyst. This could be corner radius less than 100 m at third and how much time spent in this one. Then, this time is counted as valid event, the zeroes are removed and the cumulative values are done. Another example is the time spent at full throttle events. If each ones counts as 1 and partial throttle event counts as 0.5, the cumulative is the sum of all those values. Since it is possible to accumulate any channel, the gating can be done. After the cumulative, the value obtained is divided by the amount of valid events. Hence, it is also possible to perform the cumulative of the full throttle only of the partial one. These can be plotted in order to evaluate a lap. In addition, this data can be overlaid with respect to the cumulative of other laps. Hence, it is possible to perform comparisons. An important detail with multiple laps plot is, that each lap has a different lap time, number of events and valid events. In addition, lap distance is a cumulative channel, it is different each lap. This always have at least a wheel locking, different race line or a wheel spinning.

Throttle acceptance

Figure 5 illustrates two approaches to evaluate the throttle acceptance, one at function of speed and the other at function of the lateral acceleration. Both have their own logic. The first point is to understand that parcial throttle at either high speed or lateral acceleration are not desirable. The math channel created is speed times throttle, or lateral G times throttle. In the first case (Figure 5, upper graph), the speed times throttle is exhibited by the gray line. It is possible to notice that, it overlays the speed trace only at a specific throttle threshold, which in this case is 50%. This means that the partial throttle are being excluded. In a similar manner, the graph of the lateral acceleration times throttle exhibits Gy only when TPS indicates a value above 70%. In this case, the evaluation only accounts high corners maneuvers.

References

  • This article was based in the lecture notes written by the author during the Applied Vehicle Dynamics lectures attended in Dallara Academy;
  • Knox, Bob. A Practical Guide to Race Car Data Analysis. Rev. 1. ISBN: 978-1456587918;
  • Segers. J. Analisys Tequiniques for Racecar Data Acquisition, 1° Edição. Warrendale, PA. SAE International. 2008.