# Measurement and Modeling of a Cargo Bicycle Tire for Vehicle Dynamics Simulation
## 4 Discussion  
Within the scope of the present investigations, bicycle tires for cargo trailers were measured with the help of the MoReLab on real road surface conditions on the test track at Vauffelin. It was shown that the test truck, whose regular purpose is the automotive sector, is capable of measuring the behavior of bicycle tires. Due to the rim design and the dimensions of bicycle tires and wheels, an adapter rim had to be used for the measurements, which does not allow for the same positioning of the wheel compared to car or truck tires. As a result, a lever arm was introduced that led to crosstalk effects, which needed to be corrected. It could be shown that the crosstalk can be compensated using the method of [22], so that the measurement data of \(T_{t,z}(\alpha)\) follow the base curve according to [16]. Due to inaccuracies in setting the zero position of the slip angle as well as the occurring lever arm, a small measurement error arose in the measurements of \(F_{t,y}(\alpha)\) and \(T_{t,z}(\alpha)\) in the case of horizontal shift. A correction was made during modeling by selecting the boundary conditions. Within modeling, the MF according to [16] was used, and its coefficients were determined by optimization. Due to the described shift, boundary conditions for the coefficients are defined in such a way that the models corresponded to the physical theory. Since the slip angle \(\alpha\) can be set from \(-2^{\circ}\) to \(18^{\circ}\) using the test truck, the measurements for the positive range of \(\alpha\) visualize the saturation of the tire. The experiments complement the investigations according to [14], which cover a smaller slip angle range, although these were carried out for a different tire type and the use of the camber angle \(\gamma\). To improve the modeling accuracy of \(F_{t,x}\) and to reduce the slightly increased RMSE, the MF coefficient \(H\) according to [16] can be used in further analyses to improve the sharpness of the curve. The influence of the tire pressure could be investigated at different normal forces. The lower normal force \(F_{N,z}\) was limited by the test system, so that the intended lower normal force of 500 N could not be adjusted. For further investigations, a second analysis at a lower normal force than 625 N would be appropriate in this context. At a contact force of 765 N, the tire pressure had a significant influence on the maximum transmittable longitudinal and lateral forces. In contrast, the change in the gradient of the linear range at the same normal force was small. We plan to investigate the impact of tire pressure on the longitudinal and lateral forces by a subsequent analysis of the contact area. Further, it should to be noted that the present investigations were carried out with a camber angle of \(\gamma=0^{\circ}\). If the presented models are used for the simulation of a bicycle, e.g. a cargo bike, the impact of camber on the longitudinal and lateral forces must be taken into account. Ref. [13] provides detailed information regarding this behavior. An essential aspect of tire modeling within the development of the drive control of an electrically propelled bicycle trailer is made clear by integration into the V-model. At present, most product development processes generally follow the principles of model-based systems engineering (compare, e.g., VDI 2206 [25; 26]). This means that models continuously accompany the entire processes and are used for simulation for verification and validation purposes. In industrial companies, current product development processes usually apply model-based systems engineering (MBSE). The inherent procedural logics in such processes can be depicted in a so-called V-model (compare VDI 2206 [25]) and can be seen in Figure 14.  
The main logical path in a V-model shows the progression from the requirements (e.g., permissible cargo weight) formulated for one technical system (e.g., a cargo bicycle trailer) over the intermediate steps such as the implementation of system elements to the final realization of the system.