# Measurement and Modeling of a Cargo Bicycle Tire for Vehicle Dynamics Simulation
## 2 Materials and Methods
### Measurements
#### 2.1.1 Mobile Tire Testing Laboratory
Furthermore, the system offers various variable parameters that can be set by the operator for different experiments with the test truck. These include:  
* Normal Force \(F_{N,z}\), which depends on the mass distribution of the vehicle. \(F_{N,z}\) results from the average value of \(F_{t,z}\) in \(F_{N,z}=\bar{F}_{t,z}\). ;
* Longitudinal speed \(v_{v,x}\) at which the measurements are to be carried out;
* Slip angle \(\alpha\);
* Camber angle \(\gamma\). An overview of the measurement system up to the raw data output is shown graphically for the test truck in Figure 2. The measured variables described above are collected via the sensors, sampled by the central computer in the test truck, and provided with a time stamp \(t\). The merged data are stored and can be saved as raw data after the completion of a test. The recorded raw data serve as a starting point for the upcoming post-processing. For a better understanding, Figure 2 also shows the speed control loop of the hydraulic drive. Here, the target wheel speed \(\omega_{ref}\) required by the user, depending on the case, is transmitted from the central computer to the PLC. The PLC then calculates the displacement volume \(V_{g}\), which serves as the control variable for the hydraulic drive. This results in a wheel torque \(T\), which acts on the system and, in turn, influences the actual wheel speed \(\omega\)  
Figure 2: Overview of measurement and drive control system. The control loop is completed by measuring \(\omega\) using a wheel speed sensor and transmitting this to the central computer of the test truck. As the MoReLab was developed for the automotive sector, measurement rims from a diameter of 13 in (330.2 mm) upwards with an offset of 60 mm is used as standard. The diameter of 13 in (330.2 mm) results from the size of the measurement hub, which would interfere with the measurement rim at smaller diameters. The offset 60 mm ensures that the center contact point of the tire \(P_{p}\) is in line with the center of the measurement hub. This prevents the development of unintended torques from resulting lever arms and therefore reduces the occurrence of crosstalk. Due to the research of [13], which claims that the measurement of bicycle tires should be as realistic as possible compared with the real use-case, a special adapter rim for 20 in (508 mm) wheels with spokes was used. The spoke length of the adapter rim was the same as the spoke length of the wheel-motor combination often used in electrified trailers and equals 75 mm. However, the diameter of the adapter rim was almost the same as the diameter of the measurement hub, which only allows for an offset of 5 mm to be realized. This leads to the disadvantage that the contact point of the tire \(P_{p}\) was no longer in the center of the measurement hub, but shifted towards the positive \(y_{v}\) direction of the vehicle. The displacement of the tire's coordinate system (\(x_{o}\), \(y_{o}\) and \(z_{o}\)) and the measurement hub's coordinate system (\(x_{v}\), \(y_{v}\) and \(z_{v}\)) due to the respective adapter rim, as well as the resulting lever arm \(l_{o}\), are shown in Figure 3.  
Due to the lever arm \(l_{o}\), torques about the \(z_{v}-\) and \(x_{v}-\) axis arise for the case \(\alpha=0^{\circ}\) and for \(\alpha\
eq 0^{\circ}\) while driving the test truck with the tire interacting with the ground during experiments, which, in addition, leads to crosstalk in the force channels of the measurement hub. For example, if an external force is applied only in \(x_{o}\) direction, the resulting measurements will show nonzero values on all other channels. The same applies to the remaining directions in three-dimensional space. Therefore, crosstalk must be corrected by the user. Additionally, an offset compensation must be carried out. If the data have a large amount of scatter, smoothing or averaging can be used to reduce this effect.