# Measurement and Modeling of a Cargo Bicycle Tire for Vehicle Dynamics Simulation
## 3 Results
### Post-Processing  
Figure 6 presents the data of test no. 3.1. The diagram is divided into the results of the acceleration and braking tests that cover \(F_{t,x}(\kappa)\), which are listed in Figure 6a. The results of the steering test are shown in (b) as \(F_{t,y}(\alpha)\) and (c) shows the relation \(T_{t,z}(\alpha)\). In a first step, the raw data are analyzed more closely, which is visualized as a black point cloud and shows a large scatter for \(F_{t,x}(\kappa)\), \(F_{t,y}(\alpha)\) and \(T_{t,z}(\alpha)\). This results, in part, from the not exactly reproducible environmental conditions, such as the asphalt condition, tire wear or the temperature. In addition, there is a fluctuation in the contact force \(F_{N,z}\) that the test truck exerts on the tire. The pneumatic adjustment of the contact force must be repeated after each tire change. A noticeable behavior can be seen in diagram (c), which shows the drift of the raw \(T_{t,z}\) data when the slip angle \(\alpha\) is larger than \(8^{\circ}\). It is assumed that the crosstalk of the measurement system is responsible for this effect, since investigations according to [16] specify a different shape of the base curve of \(T_{t,z}\). In contrast to the base curve, which generally has two zero crossings and a minimum in-between, only one  
Figure 5: Post-processing chain. Figure 6: Measured and post-processed data of test no. 3.1 where (**a**) shows \(F_{t,x}(\kappa)\), (**b**) shows \(F_{t,y}(\alpha)\) and (**c**) shows \(T_{t,z}(\alpha)\). zero crossing and a subsequent drifting of the \(T_{t,z}\) curve in the direction of \(-\infty\), as can be observed in the raw data. The proof of this assumption is provided by the crosstalk correction described later in this section. After its application, the \(T_{t,z}\) data show a second zero-crossing and a minimum between the first and second zero-crossing, as can be seen in Figure 6c. To draw conclusions about the real behavior of the tire from the data, the offset of the measurement system is compensated first. Within the scope of the offset correction, an attempt is made to compensate the measurement error of the system which results, for example, from hysteresis. For this purpose, load-free conditions are set before and after each measurement series, so the unloaded condition offset of the force channels can be measured. Resulting offset values for test no. 3.1 are listed in Table 2. The recorded offsets of \(F_{t,x}\), \(F_{t,y}\) and \(T_{t,z}\) before and after the measurement series of one test case, e.g., driving for test no. 3.1 are used to calculate a straight line passing through the offset points. Subsequently, this straight line is subtracted from the measurement data. Offset-corrected and RLOWESS smoothed data are represented in Figure 6 as a dark gray point cloud. Since the offset data are recorded for the force sensors, but not for the measurement of torque, diagram (c) does not show an offset-corrected dataset. The offset still existing after the compensation, especially for the measurements of \(F_{t,y}\) and \(T_{t,z}\), results from a default setting of \(\alpha\) and \(\gamma\) of the measurement equipment, which is not exactly at \(0^{\circ}\). A more precise setup of these parameters is not possible. Compared to the raw data, the offset-corrected data of \(F_{t,x}\) and \(F_{t,y}\) show a similar linear trend at the beginning. However, with the beginning of the non-linear range at \(\kappa\geq 4\%\) or \(\alpha\geq 5^{\circ}\), the deviation of the graphs increases. At this point, the offset corrected graphs exceed the mean of the raw data. This behavior is particularly clear when looking at \(F_{y}\) for \(\alpha\geq 12^{\circ}\). Considering Table 2, this behavior can be explained as the offset measurement of \(F_{y}\) after the test case \"steer\" is far below 0 N. The same applies to all other axes, whose values after the test cases deviate further from 0 N than the values measured before the test case.