# Measurement and Modeling of a Cargo Bicycle Tire for Vehicle Dynamics Simulation
## 2 Materials and Methods
### Measurements
#### 2.1.2 Tire Parameters and Test Matrix  
The chosen tire model is called \"Pick-Up\", from the company Ralf Bohle GmbH, distributed by the brand name Schwalbe(r), which was specially developed for use in cargo bikes or trailers. The tested size of 55-406 ETRO (\(20\times 2.15\) in) is a common tire choice for these applications. According to [17], this tire can be inflated with an air pressure  
Figure 3: Measurement hub with offsets of bicycle rim and tire (**a**) yz-plane view (**b**) xy-plane view (**c**) xy-plane view with \(\alpha=18^{\circ}\). of 2.5-4.5 bar (35-65 psi) and should mainly be used on asphalt or light gravel roads. In addition, the tire has a double wire carcass and puncture protection. The weight is listed as 0.790 kg. The tire mounted with an inner tube on the adapter rim is shown in Figure 4a. A view of the profile before tests were carried out can be seen in Figure 4b. While many external influences impact the tire, the air pressure is an essential parameter that can be adjusted directly on the tire, on the valve of the inner tube. In combination with the setting options of the test truck, this results in numerous variable parameters, which are listed in Table 1. To investigate the effects of tire pressure on the forces that can be transmitted, the pressure was selected within the range permitted by the manufacturer. The investigated tire pressures were 3.0, 3.5 and 4.0 bar. Since cargo trailers are intended for the transportation of heavy loads, the measurement of the tires was planned with a lower normal force of 500 N and an upper normal force of 750 N. However, the measurement equipment does not allow for fine adjustment, so the closest possible range of approx. 625 N as the lower and 765 N as the upper normal force was applied during the tests. Assuming an acceleration due to gravity of 9.81 \(\frac{m}{s}\), this corresponds to a load of around 127 or 156 kg optimally distributed at the center of gravity for a trailer with one axle and two wheels. As cargo trailers are mainly operated with electrically assisted bicycles with an assistance of up to 25 km/h, the working range was assumed to be 20 km/h or 5.56 m/s, respectively. Therefore, the investigations were carried out at a constant speed of \(v_{v,x}=5.56\) m/s of the test truck. Furthermore, the slip angle \(\alpha\), which can be adjusted by the system from \(-2^{\circ}\) to \(18^{\circ}\), was completely utilized. Since the present work essentially focuses on the investigation of bicycle tires for cargo trailers, which do not offer a camber angle or the possibility of tilting the tire into the curve, all investigations were carried out with a camber angle \(\gamma\) of \(0^{\circ}\). In this context, it must be noted that the measurements and the model derived from them are only representative for \(\gamma=0^{\circ}\) on an even road surface. On uneven road surfaces, the vertical line of the contact patch is not in line with the tire centerline in the yz-plane, resulting in \(\gamma\
eq 0^{\circ}\). As the field of application for load trailers is mainly in urban areas, this case was not considered a priority in the present investigations. Figure 4: Tested tire (**a**) mounted on adapter rim (**b**) view of the profile. As a result, Table 1 shows a total of six parameter combinations for measuring the tires. For each of the six combinations \(F_{t,x}(\kappa)\), \(F_{t,y}(\alpha)\) and \(T_{t,z}(\alpha)\) are captured. Since \(F_{t,x}(\kappa)\) has to be measured for driving and braking while \(F_{t,y}(\alpha)\) and \(T_{t,z}(\alpha)\) can be measured in the same steering case, the six parameter combinations of Table 1 must be multiplied with the three test cases (drive, brake, and steer) to obtain a total number of 18 test cases. From the experience of previous studies, each of the 18 test cases were found to require between 15 and 25 measurements to record an average representation of the behavior.