Hermeneutics is a term that refer to the act of interpreting data. Hence, maybe it is possible to infer that race car data analysis is the hermeneutics of the vehicle behavior. In race car data analysis the objective is to understand the vehicle behavior in order to reduce ΔT. Consequently this is used to answer some questions and make comparisons with other drivers, cars and laps. Usually in the motorsport field the professional responsible for the data acquisition is data acquisition guy, or just DAG. The racing engineer and DAG are normally are different positions. The first deals with the driver, while DAG is responsible for the analysis of the database. Frequently telemetry is referred as the data which is being analyzed, but this is the data see live on the monitors, while the car is racing. In the racing field, the data acquisition systems are based in six parameters, engine revs (RPM), vehicle speed, throttle position, steering angle, lateral and longitudinal accelerations (G_y and G_x, respectively). This article proposes a brief introduction about the data acquisition systems adopted in race cars and their principles.

What is data analysis ?

The main difficulty of the data acquisition analyst is the ability to convert a subjective or imprecise language into quantitative measures. The driver used to have this job in the past since there was any data acquisition system. Nowadays, its role was reduced to just drive as fast as possible. Figure 1 illustrates the pyramid that describes the usual path of data analysis. It starts with raw information or data, which are just numbers. However, when this data is being considered inside a context, it becomes an information. This is basically a structured or organized data. When information gains a meaning, it becomes a knowledge, which is about past events. Hence, this generates an insight, which becomes a wisdom. Since always there is a purpose, this finally becomes a decision. The most important point is to be aware in which step of this pyramid the analysis is. Therefore, the raw data without a proper context is just a collection of data. The context is necessary to explain the data.

Breaking the information

Handling is a term frequently used in many areas of the motorsport field. In racing, handling is essentially yaw, lateral dynamics and balance. Hence, it is a term that refers to the vehicle dynamics in corners. The data comes from track and/or simulators. This last one is a data generator. The driver drives the simulator and the data is logged virtually. The simulator, or drive-on-the-loop, is not only a tool to evaluate different setups and configurations, it is also a source of data that usually is difficult to measure in track tests. For instance, slip angles, wheel loads (vertical loads) and the tire grip force. These are all interesting parameters that are very difficult to measure in the real environment. Data analysis is not simulation, instead it is the interpretation and evaluation of the data. In addition, it is a synthesis since the data analysis looks to break the information in small pieces in order to provide a better understanding. Synthesis is the opposite of analysis, it looks to derive the big detail from small data. For instance, when the process looks for numbers, it is analytical, when it searches for a behavior or a final parameter, it is synthesis. Data analysis is the understanding of past events through patterns and signals.

Vehicle dynamics

The data analysis deals with the amount of information that comes from the vehicle dynamics. Figure 2 illustrates the three main analysis, ride, handling and performance. It is possible to notice that in all of them there are some degree of roll. These are usually the effects of the load transfer. Actually, these are also due to the fact that each wheel is measured independently. Hence, the differences between wheels from the same axle occur due to rolling. Therefore, the roll can be considered a sort of coupling dynamics, because without roll those maneuvers would be completely decoupled, independent.

Weight influence

Another important aspect for vehicle dynamics is the weight. This is a strong concern in terms of stiffness, structure and design. The are refers to the effects on downforce and drag. Tires are the interface, but also what concern the vehicle dynamicists. Hence, the vehicle is subjected to its weight and aero forces and tire develops grip in function of these (Figure 3). The job of the vehicle dynamicist is to take into account the design, the aerodynamics, the powertrain and the tires in order to generate the maximum amount of grip. This means that for a given mass it is generated the maximum amount of acceleration. The best vehicle dynamicist is able to extract the maximum acceleration from a given mass, a vehicle, because grip (Figure 3) is a force, this is applied to a mass becames acceleration. Hence, racing is the generation of the maximum amount of acceleration for a given mass. The difficulty of a race is its hyperstatic behavior due its four contact points. The second difficulty is the contact media, the tires are highly non-linear. The third one is that this non-linearity varies with temperature. The last difficulty is the track, which never is the same.

Globally, for non-aero cars, the lateral acceleration (G_y) is in the same order of magnitude of the friction coefficient. The reason it that the vertical load (F_z) is equal to the vehicle weight. In a car with aero, G_y is the same, but the lateral grip (F_y) is different (Figure 4). This is the friction times the vehicle loads, which is the aero loads (A) and the weight together. Hence, the lateral acceleration is described by the expression seen in Figure 4. It is higher than 1, thus higher than the friction coefficient (μ). Therefore, the grip resist the mass only, the downforce is a weightless physical force. This is the reason why the downforce is necessary to achieve high lateral accelerations.

Bi-cycle model

The most common vehicle model used for data analysis is bi-cycle model, as seen in Figure 5. One of the main equations is the side slip angle one:

β = (b/R) – α_r

The side slip angle, apart from b/R quotient, is only related to the rear slip angle. The side slip angle is the car rotation around its center of gravity (CoG). Hence, β is a function of α_r only. The second main equation is the steering wheel angle. Apart its constant value L/R, it is a function of the difference between front and rear slip angles:

δ = (L/R) + α_f – α_r

β and δ are car parameters, while α_f and α_r are tire parameters. The bi-cycle model can be described either in terms of slip angles or in terms of steering and side slip angles. If it is possible to measure α_f and α_r, then the steering and the side slip angles are obtained. Conversely, if it is measured the steering and the side slip angles, then it is found the slip angles. These considers that the assumptions are the bi-cycle model and the steady-state movements. The difference between the front and the rear slip angles is the car balance. Usually this is defined as understeer and oversteer, these are a stable and an unstable equilibrium, respectively. Hence, understeer and oversteer refer to equilibrium stages, thus the balance of the car is judged in terms of steady-states.

It is not possible to spot understeer by the steering input δ. Actually, this is spotted by the graph on Figure 7. An important relation is the one for the lateral acceleration, which is highlighted in Figure 7. This the speed times the sum of the derivative of the side slip angle and the yaw rate. Since it is being considered a series of steady-state movements, the derivative of the side slip angle is zero. Hence, the lateral acceleration is only accounted by the yaw rate times the vehicle speed. In this equation, the speed and the yaw rate can be measured by sensors, which means that it is possible to calculate the derivative of the side slip angle. The integral of this parameter results on the side slip angle. Hence, the graph is seen in Figure 6 can built. In a corner event, the values of these parameters vary according to is seen in Figure 7.

Before entering in the corner, the side slip rate is equal to zero, thus its integral is also zero. At the corner end, the side slip rate is zero again. However, if the integral is done from the corner entering until the end, it is possible to get the residual value for each corner. Hence, a critical estimation of the side slip angle can be obtained, thus the tire slip angles. The bi-cycle model is defined as a series of steady-state movements due to the lightweight characteristics of race cars. Transient effects refer to inertia effects, thus the yaw accelerations and longitudinal accelerations. Since race cars are light, the inertial effects are reduced. Hence, it is possible to approximate every movement sequence as a series of steady-states ones. However, there are some situations for race cars that can be defined as transients. These are wheel spin, vehicle spinning and when the car goes out of the track. The reason is that the vehicle dynamics for race cars deal with low frequency movements in order to reduce the transient effects. This is possible, because race cars are light. More mass means more acceleration and time for the car changes its speed. For road cars this assumption can not be made since the mass is higher.

References

• This is article was written based on the lecture notes written during the Applied Vehicle Dynamics lectures attended at Dallara Accademy.