## 3 Results
At a given vertical load, its value will depend only on the contact area of the tire with the ground. In turn, this parameter will depend on the size of the tire's cross-section near its contact with the ground. Based on the literature data, it is known that radial tires will react differently to changes in this cross-section compared to bias-ply tires. For this reason, it becomes justified to analyze both the cross-section of the tire and the footprint areas. The first of these parameters is shown in Figure 5. The cross-sections were made at the height corresponding to the higher transverse deformation of the tires. Among all the analyzed cases, the smallest changes in cross-section due to the increase in inflation pressure were found for a bias-ply tire with a lower level of vertical load. In this case, the first increase in inflation pressure resulted in an increase in the cross-section area of less than 0.02 m\({}^{2}\) (10.0%), while the subsequent increase in inflation pressure did not cause any changes in the cross-section area. In turn, for the same tire with a higher vertical load, the first increase in pressure resulted in a decrease in the cross-section area of 0.03 m\({}^{2}\) (12.4%), while a further increase in the inflation pressure resulted in an increase in the cross-section area of 0.02 m\({}^{2}\) (8.1%). This tendency may be caused by the fact that when the inflation pressure was first increased, deformation occurred in the radial direction (the effect of \"tightening\" the side walls), and only when the inflation pressure was increased again did significant transverse deformation occur, resulting in an increase in the cross-section area. In the case of a radial tire with both vertical loads, a decreasing tendency in \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Tire/Vertical Load** & **Regression Equation** & **Coefficient of Determination** &
\begin{tabular}{c} **Coefficient of Correlation** \\ **(r-Pearson)** \\ \end{tabular} \\ \hline Bias-ply, 11.8 kN & \(\text{y}=-1025.0\text{x}^{2}+443.4\text{x}-15.5\) & 0.98 & 0.99 \\ \hline Radial, & & \\ 11.8 kN & \(\text{y}=-964.1\text{x}^{2}+377.1\text{x}-14.3\) & 0.98 & 0.99 \\ \hline Bias-ply 19.6 kN & \(\text{y}=145.1\text{x}+7.53\) & 0.98 & 0.99 \\ \hline Radial, & & \\ 19.6 kN & \(\text{y}=107.8\text{x}+1.62\) & 0.98 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the regression analysis between the footprint depth and tire inflation pressure. the cross-section can be seen with increasing inflation pressure. Greater decreases (25% and 11%, respectively, for both inflation pressure increases) were found at lower vertical loads. At higher loads, the decreases in the cross-section area were 7% (first pressure increase) and 8% (second pressure increase). This was probably caused by the fact that the heavier tire became less deformable due to initial deflection. The regression analysis performed for each tire/load combination (Table 5) showed that only for a radial tire with a higher vertical load was it possible to use linear regression. In other cases, the relationship between the inflation pressure and the cross-sectional area was described with a second-degree polynomial function. This situation was, therefore, similar to that in the case of the footprint length parameter, so the change in the footprint surface is directly related to the change in its length. As mentioned in the previous section, one of the most important parameters of cooperation between the wheel of an agricultural vehicle and the ground is the surface of the generated footprint. The values of this parameter are shown in Figure 6.  
In the case of the last analyzed parameter, the highest values were found at a higher level of vertical load (19.6 kN).