In the third article about the math channels for race car data analysis it will be discussed the ones derived from the engine data. These usually describes some important behaviors of the car, as the understeer. In addition, it will made summary about the derivatives that can be created with the basic channels. The effects of the tire radius and load transfer can be also accounted using math channels, even a simple tire model.

Engine channels

Another important details that can be analyzed through the basic signals are the engine torque and the definition of engine rev limit, also if this is a hard of a soft one. The engine torque can be derived from the longitudinal acceleration (G_x,a_x). This one multiplied by the vehicle mass results on the traction force. Then dividing this by the wheel radius results on the toque. Hence, through the transmission efficiencies and the engine revs it is possible to build the engine toque channel. It is important to have the main data to create some other important channels. For instance, the wind tunnel can provide some information about the drag coefficient C_xS and the aeromaps. Then it is possible to estimate the drag since the speed is already known.

The influence of the slip angles

An interesting point is how to have some idea of the slip angles by using the understeer channel. Assuming that the car races at a sequences of steady-state, the distances from the center of gravity (CoG) to the front and rear axles are known, thus for a given lateral acceleration (G_y,a_y) and vehicle mass, it is possible to calculate the tire grip. After that, this is splitted between front and rear thanks to the weight distributions. Hence, it is possible to obtain the front and the rear grip. Then, these are multiplied by the slip angles of front and rear wheels and the speed. The tire drag is obtained. Usually, the front and the rear lateral grip correspond to the weight distribution, except when the car is under transients. Therefore, considering the lateral acceleration for small angles as given by the following formulae:

a_y ≡ V∙(ψ’ + β’)

The turn radius is calculated by:

R_ay = V²/a_y

Or:

R_ψ’ = a_y/ψ’²

Hence, it is possible to plot both turn radius formulas once the yaw rate (ψ’) is known. Now it is possible to evaluate if the car is under steady-state or transients. If both R_ay and R_ψ’ result on the same signals, the vehicle is under steady-state. Conversely, if R_ay and R_ψ’ result on different plots, the car is under transients. However, to be able to identify these behaviors, it is required a yaw rate sensor. The importance of this consideration about the slip angles, is that as higher these are, higher will be the longitudinal component against the movement. Hence, high slip angles consumes engine torque.

Defining the engine torque

Therefore, engine torque is important for straight line movement. Part of this is absorbed by aero loads, rolling resistance and tire drag. High speed corner are when the slip angles are important. Hence, the engine torque is a net of the lateral forces. The engine torque is the traction force times the wheel radius as seen on the formulae:

T = F_tr∙R_wheel

Hence, there are different demands for this torque, the traction due to the drag, the rolling resistance and the tire drag. Finally, it is possible to write the following relation:

[(T – T_absorbed)/W]∙a_x

With this relation, it can be identified the amount of the engine torque which is being used. The driveshaft, shafts and the clutch torque sensors are helpful for their losses calculations. Once the information about gear and revs are known it is possible to program the rev limiter. For this, it is important to understand that at different gears, the car has different equivalent mass. This is a parameter that is equal to the mass plus the gear. Hence, the equivalent mass is a channel that can also be plotted.

Under torque

The under and the over torque are situations which the engine revs at the gear shifting moment are too low or too high, respectively. This information is usually plotted according to the throttle signal. For example, Figure 1 illustrates the conditionals fo the under torque signal. If the throttle is more than 90% and the rev signal is higher than the threshold, the first part of the conditional goes to 1. However if the revs signal is lower than the threshold, then the under torque value becomes – 1. This is quite synthetic parameter that graphically indicates if the gear shifting was performed at the correct moment. Hence, it is important to set the under torque channel in the range of the best engine torque one.

At the top gear, the engine is in a narrow range, while in lower gear, it is in a wide one. This means that those limits for the under torque channel change according to the gears. Hence, it is interesting to program the under torque to be modified at each gear. The reason for this adaptation is that each gear has a different engine rev time. At the first gear, for instance, this time is very high.

Event counter – Gating

The gating procedure is a way to devise a math channel to calculate the minimum, the average and the maximum speeds only for specific events. It is important to count the events when the car is under corners, in order to have some stats for the meaningful events. For instance, in 50 Hz gating, there are 50,000 numbers. If 60% of the events on the are corners, thus 30,000 number referring to cornering events for a 100 s lap. Hence, a channel which the output is 0 or 1 is created. The conditionals are established, which can be a_y > 1 G as a cornering event, thus it counts 1. Another important detail is to calculate the cumulative of these events according to the speed. At the end, the sum is performed and divided by the 30,000 meaningful events and also the average, the maximum and minimum speeds.

Examples of gating

This can be done for cornering, braking, acceleration, full throttle, under torque, understeer and oversteer. There are many possibilities. Some interesting ones are the steering events. These can be combined with the throttle to identify which the car is steering and on throttle or steering and off throttle. This last one counts the mid corner events. In addition, it is possible to calculate coasting, when the driver is not cornering, braking or accelerating. In this case, the values for accelerating, braking and cornering will be all zero.

Throttle acceptance

The throttle acceptance is represented at Figure 4 in some ways. First, the red circle indicates a section which the driver or the car is reluctant to reach or to accept full throttle respectively. Then, there is a graph on the left-bottom side with the throttle, the speed and the throttle acceptance channels. The throttle signal multiplied by the speed signal results in the throttle acceptance. It allows to identify the points which are off throttle on the speed trace. It is possible to create this channel for off throttle on the lateral acceleration trace. The most crucial events are the ones that occur at high speeds, as when the driver hesitant on the throttle. The same at low speed are not so critical, rather it can be intentional since oversteering at this situation is acceptable. However, hesitation at 240 – 300 kph are dangerous. For this reason it is important to build a graph as the one at the left-upper side of Figure £, the plot of the speed against throttle. As can be seen, there are relevant situations at partial throttle at high speed. The difficulty of the data acquisition guy (DAG) is to put into graphical forms a concept. Since throttle acceptance is a channel that indicates how easy is to apply full throttle, the speed and TPS signals should be plotted. In ideal situations, the yellow highlighted zoe in the left-upper side graph of Figure 4 is not allowed, because it represents parcial throttle at high speed. For instance, in this section it is taken as an example the points at 150 and 170 mph. Extending these to the time-distance graph, it is possible to track the region of difficult throttle acceptance. This is the first step to spot the problems that can result in low capability to accept full throttle. In terms of gating events, the meaningful events for the throttle acceptance is segregated in the range between 20 and 80 % throttle signal. Once this is done, it is possible to weight those values by the speed channel. This allows to penalize the events which the driver hesitant to obtain full throttle. Hence, it is possible to count the events which the throttle signal is between 20 and 80 % and make the cumulative of all partial throttle events weighted on speed.

Figure 5 illustrates another situation that the throttle can be helpful. As can be seen, the blue, red and green curves mean on-off throttle, braking and steering, respectively. These are channels created in order to describe if these commands are being activated. Conditional functions are used as, above 1 G deceleration it is considered braking, if throttle is above 80% it is accounted as throttle on and if the steering modulus is higher than 5° it is considered steering on. These are 0-1 channels. Then, it is created a channel that accounts all these channels, thus it is possible to visualize how many of these commands are activated. Hence, this channel, represented by the black line, can deliver values as 0, 1 and 2. The first means no throttle, no braking and no steering, thus coasting. Usually, this channel does not return 3, because it is not possible to do those three actions. However, 1 or 2 are usual feedbacks. 1 could be only throttle, braking or steering, while 2 is the combination of two of these. Except, throttle and braking at the same time. In Figure $ it is indicated a situation that there is no throttle, no braking and no steering. However, it is possible to notice that there is a partial throttle application and no steering. This last one could be due to the fact that the car is racing through a S-curve. It is interesting to notice that the throttle signal is about 73% and if the range of the partial throttle gate was 60%, this situation could no be spotted.

Another math channels

There are few more math channels that are interesting to be used. One of these are the brake pressures. These can be used to create the brake bias channel, which is the ratio between the front and the rear brake pressure signals. Another interesting channel is the steering speed and the steering rate, which the time derivative of the steering signal. The data acquisition software uses the lap time as the base for the time derivative function. The steering speed is an useful tool to evaluate how the driver is using the steering wheel. For instance, if the steering speed is too high, this could not be good for tires. In case of too low steering speed, the driver can feel scary since the car is too low to enter in the maneuver. Hence, there is a proper steering speed. The third parameter illustrated in Figure 6 is the throttle speed. This is the time derivative of the throttle signal and means the speed which the driver activates the gas pedal. This channel allows to observe how the driver manages partial throttle situations. Hence, the throttle speed allows to spot situations as the one highlighted at Figure 6. In this case, it is possible to notice that the driver could be more gentle on the the throttle activation.

Tire radius influence

Another important parameter is the tire radius, this is important to compute the wheel load, the centrifuge and the tire pressure. Actually, tire radius is important for speed corrections and ride heights, because in the spring deflection and motion ratio account the spring mass, but miss the tire deflection. This is basically the variation of the wheel radius, thus the ride heights can be predicted. The damper speed is usually obtained by the derivative of the spring deflection. However, it should be carefully done since damper and spring can have different motion ratios.

Load transfer measurements

The anti-roll bar loads can be obtained by the measure of the drop links through load cells or strain gauges on the anti-roll bars. The load transfers can be defined as the mass of the car times the lateral acceleration, the longitudinal acceleration and the center of gravity (CoG). Another way to measure the load transfer is by load cells on the push rods.

Slip ratio accounting

The tire longitudinal slip is another interesting parameter that can be created. Figure 7 illustrates an example of its application. It is required at least two speed sensors. However, to be more precise, four speed sensors are mandatory. The data analyst should define which of those will be used as signals for the formulas seen in Figure 7. In the case of braking situations, it is expected to have a lot of slip on the front wheels. Hence, the rear wheel sensor are used as the reference velocity and ω is accounted by the front wheel sensor. For the case of the longitudinal slip in traction, the configuration of the channel is different. It is expected that the rear wheel are slipping, thus the front wheel sensor will be used as the reference speed. The rear wheel sensor is used on ω. The switching between braking and accelerating slip ratios can be coded by the sign of the longitudinal accelerations. Another way to switch between front and rear slip angles is considering what happens in the two maneuvers. For instance, in braking the inner front wheel is locked, thus one of the two speed will be low. Hence, the braking is given by the sign of the longitudinal G. With parameters multiplied by the mass, it is possible to compute the grip in braking and in traction. Hence, it is possible to create a simple tire model. The same approach can be done for lateral grip. Since it known the yaw rate (ψ’), the slip angles (α), the side slip angles (β’) and the lateral acceleration ay, it is possible to create a simple tire model. In addition, it is possible to add the variation of the vertical loads. A simple tire model created only with math channels and empirical formulas. This is useful since tire manufacturers do no provide any data. Hence, the car and the track interactions together with this tire model is used as a sorte of tire data generator.

Conclusion

This article discussed the main parameters derived from the engine channels. The understeering is very useful when combined with the throttle signal, it can supplement a theory about the understeer behavior. The under torque channel helps to evaluate the driver gear shifting. The math channels expand the data acquisition and analysis activities. However, it should be considered the limitation at some tools created from these.

References

• This article was based in the lecture notes written by the author during the Applied Vehicle Dynamics lectures attended in Dallara Academy;
• Segers. J. Analisys Tequiniques for Racecar Data Acquisition, 1° Edição. Warrendale, PA. SAE International. 2008.