# Measurement and Modeling of a Cargo Bicycle Tire for Vehicle Dynamics Simulation
## 2 Materials and Methods
### Measurements  
#### 2.1.1 Mobile Tire Testing Laboratory  
The MoReLab, which can be seen in Figure 1, is a truck with two possible test wheels that can be mounted in the middle between the front and rear axles on each side. A special measurement hub with load cells was used to record longitudinal and lateral forces, as well as torques acting from the tire towards the hub. The signals from the measurement hub were sampled and recorded at a frequency of 250 Hz and contain:  
* Longitudinal tire force \(F_{t,x}\);
* Lateral tire force \(F_{t,y}\);
* Vertical tire force \(F_{t,z}\);
* Torque around x-axis \(T_{t,x}\);
* Torque around z-axis, also referred to as aligning torque \(T_{t,z}\). The test wheel was propelled by a hydraulic drive, which enables the wheel to be operated even at high slip values. Because of this, even unstable slip ranges can be measured accurately. Since the drive shaft does not have an external brake, the torque \(T_{t,y}\) could not be measured with this setup. Because the truck can move on almost any surface, real test tracks can be driven with the vehicle. Compared to the indoor test benches listed in [13; 14; 15], this leads to some advantages and disadvantages. Measurements can be taken on surfaces ranging from asphalt to very coarse gravel, while gravel in particular cannot be optimally reproduced in indoor systems. However, indoor test facilities create comparable initial conditions, while the tests with the MoReLab are carried out outdoors under changing but real environmental conditions. Possible measurements that can be carried out with the presented system are listed below:  
* Spinning the test wheel faster than the truck's constant speed \(v_{v,x}\) and recording \(F_{t,x}\) respective to the longitudinal slip \(\kappa\) (driving);
* Spinning the test wheel slower than the truck's constant speed \(v_{v,x}\) and recording \(F_{t,x}\) respective to the longitudinal slip \(\kappa\) (braking);
* Steering the freewheeling test wheel with a slip angle \(\alpha\) from \(-2^{\circ}\) to \(18^{\circ}\) with the truck driving in a straight line to record the Force \(F_{t,y}\) and aligning torque \(T_{t,z}\) (steering);
* Combined measurements of spinning the wheel faster or slower than the truck's constant speed \(v_{v,x}\) while a slip angle \(\alpha\) from \(-2^{\circ}\) to \(18^{\circ}\) is applied and the truck is driving in a straight line to record the Force \(F_{t,y}\) and aligning torque \(T_{t,z}\) (steering with combined slip--not covered in this research). To capture the recorded forces in relation to the slip \(\kappa\), Equations (1) and (2) were used to calculate the slip according to the data measured by the system. Drive slip:  
\[\kappa_{d}=\frac{v_{t,x}-v_{v,x}}{v_{t,x}}\cdot 100\% \tag{1}\]  
Figure 1: MoReLab truck and measurement chamber with mounted bicycle tire and corresponding coordinate system. Brake slip:  
\[\kappa_{b}=\frac{v_{v,x}-v_{t,x}}{v_{v,x}}\cdot 100\% \tag{2}\]  
For this purpose, the measurement system of the test truck provides the measured wheel speed \(v_{t,x}\) of the test wheel to the user, which is calculated with the aid of Equation (3). \(r_{e}\) is defined as the measured effective rolling radius of the tire at the examined speed and \(\omega\) is the wheel speed measured by hall sensors. \[v_{t,x}=r_{e}\cdot\omega \tag{3}\]  
The actual longitudinal speed of the test truck \(v_{v,x}\) was recorded with the aid of a laser surface measurement. To relate \(F_{t,y}\) and \(T_{t,z}\) with respect to the slip angle \(\alpha\), the system can measure this angle directly during measurement using an analog angle sensor, which is mechanically connected to the measurement hub. It must be noted that the mechanical design of the test truck does not allow for \(\alpha\) values smaller than \(-2^{\circ}\), as otherwise the wheel mount and test wheel may collide. This also applies to the positive range of \(\alpha\), where the wheel can be turned up to \(18^{\circ}\) degrees. A range of \(-2^{\circ}\) to \(18^{\circ}\) was thus obtained for \(\alpha\).