Measuring vertical tyre stiffness of bicycle tyres

This contribution presents an analysis of the vertical tyre stiffness of 20” bicycle tyres as usually mounted on bicycle carriers for the transport of children. The current research contributes to the science on bicycle comfort with the focus on the next generation cyclists with parameter variation in type of tyre, inflation pressure, pre-load and frequency. Studying bicycle carrier comfort is an important research topic for at least three reasons. First, it is closely related to sustainable mobility, as the problem of low-emission and (sub-)urban daily mobility is often planned to be solved through an increased use of bicycles. Second, bicycle as mode of transportation is more and more in focus even for simulation tools supporting planning of infrastructure. So, there is need for empirical data for the simulation of bicycles as means of transport. Third, child transportation in bicycle carriers makes a significant fraction of child transportation by bike. Safety is often an argument for the carrier. However, there is lack of data about the vibration level. Zegelaar (1998) made comprehensive measurements of automotive tyres. He found that the vertical stiffness of rolling tyres differed from the stiffness of non-rolling tyres when excited randomly but hardly when excited sinusoidally. On bicycles Lepine et al. (2016) measured in-situ two different wheel sets on system level and could distinguish the two wheel-sets. Doria et al. (2019) measured the static vertical tyre stiffness in a larger experiment around modal analysis of a utility bicycle. They found a certain non-linear behaviour at loads around 100 N but a quite linear behaviour at higher loads, however, no tyre modes were identified. In a later experiment Doria et al. (2021) tested a numerical method to predict the comfort of a city bike and identified most of the peaks in a frequency range larger than 20 Hz. In contrast, Rothhämel (2023) found when investigating the system comfort of bicycle carriers, next to a dependency of speed and inflation pressure, peaks at 3.3 Hz and higher. In cycling there is a development to wider tyres, even in racing cycling. This contributes to a decrease of rolling resistance, however, an increase of comfort is always assumed but not yet shown systematically. Regarding bicycle carriers wider tyres (balloon tyres) are often used in combination with lower inflation pressure to increase comfort. In previous experiments lower tyre inflation pressure did not automatically correspond to decreased level of acceleration i. e. increased comfort. In this investigation we tested the vertical tyre stiffness of two different types of tyres at different pre-load and inflation pressure over a frequency range of 1 Hz to 30 Hz. One tyre was a so called balloon tyre in the ERTRO dimension 60-406, the other tyre was a narrow foldable tyre in the ERTRO dimension 35-406. Figure 1 visualises the results summarised for the balloon tyre. The vertical tyre stiffness increases as expected with tyre inflation pressure. The increase of vertical tyre stiffness over vertical load is also inflation pressure dependent. At low pressure the vertical load hardly affects the stiffness, however, at higher inflation pressure, the influence of vertical force increases. In addition, the vertical tyre stiffness increases slightly but significant over frequency. When comparing the two different tested tyres, the balloon tyre had about three times the air volume of the narrow tyre. Of course, these tyres will be operated at different inflation pressure in real life. Anyhow, to show the comparison of the stiffness at the same conditions (inflation pressure 100 kPa, vertical load 400+/-200 N, frequency 6 Hz), the balloon tyre shows a 20% higher stiffness than the narrow tyre. The full paper will show the data for both of the tyres including the mapping of the frequency dependency. Static tyre stiffness results will complete the picture.