## 3 Results

Table 2: Results of the regression analysis between the width of the footprint and the tire inflation pressure. In analyzing the changes in the length of the footprint generated as a result of changes in the inflation pressure, it can be noticed that the dynamics of the changes in the length of the footprint due to changes in the tire operating parameters were greater than in the case of the previously analyzed parameter. This trend was especially visible in the case of the radial tires. At the lowest inflation pressure and with a given vertical load, both tires had similar footprint length values (475-479 mm with a lower vertical load and 515-518 mm with a higher load). Increasing the inflation pressure in a radial tire resulted in a decrease in the footprint length, with a greater rate of decrease occurring at a lower vertical load--the decreases were 15% after increasing the pressure from 0.08 to 0.16 MPa and 9% when increasing from 0.16 MPa to 0.24 MPa (with a higher vertical load, the changes were 3% and 5%, respectively). A different tendency occurred for a bias-ply tire--with a lower vertical load, increasing the inflation pressure resulted in practically no changes in the footprint length values (differences in the range of 1-2%). With a higher vertical load on the bias-ply tire, the first increase in pressure resulted in a decrease in the footprint length of 32 mm (7%). A further increase in inflation pressure resulted in a length increase of 10.7 mm (2% compared to the length corresponding to a pressure of 0.16 MPa). In analyzing the increase in the vertical load, it can be observed that for both tires, increasing the vertical load resulted in an increase in the length of the footprints, but for the radial tire, the differences were higher than for the bias-ply tire. For example, for a bias-ply tire, the largest increase was 9%, and for a radial tire, it was as great as 27%. Similarly to the previous case, a regression analysis was performed to describe with mathematical equations the changes in the length of the footprint depending on the value of the inflation pressure--the results are presented in Table 3. \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 & y = 979.7x\({}^{2}-277.1\)x + 491.3 & 0.98 & 0.99 \\ \hline Radial, & y = 2688.3x\({}^{2}-1527.3\)x + 584.8 & 0.98 & 0.99 \\ \hline Bias-ply 19.6 kN & y = 3343.7x\({}^{2}-1202.7\)x + 593.8 & 0.98 & 0.99 \\ \hline Radial, & y = \(-260.31\)x + 537.8 & 0.97 & 0.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the regression analysis between the footprint length and tire inflation pressure. Figure 3: The values of the length of the footprint with different inflation pressures and vertical loads. Only in the case of a radial tire with a load of 19.6 kN was a linear regression equation used, with a coefficient of determination of 0.97. In the remaining cases (a bias-ply tire with both loads and a radial tire with a load of 11.8 kN), second-degree polynomial equations with determination coefficients of 0.98 were used. This fact was caused by a different type of change in the footprint length of a radial tire with a higher vertical load. There was a continuous decrease in length as a result of increasing the inflation pressure, while in other cases, only the first increase in pressure resulted in a decrease in the footprint length, and subsequent increases resulted in a slight increase. The next parameter analyzed was the depth of the footprint. The values of this parameter are shown in Figure 4.  
In the case of the footprint depth, a tendency can be noticed in which the bias-ply tire generated a significantly deeper footprint compared to the radial tire--this tendency was noticeable at both levels of vertical load.