## 4 Results and Discussion
### Comparison of the Behaviour of Finite Element Tyre Models
In the case of the simplified tyre model (R\({}^{2}\) = 0.979), \[q=0.007 pF+3.78F+545.56.\] (8)  
In the case of the complex tyre model, the mixed effect of \(p\) and \(F\) could not be demonstrated, while, in the case of the simplified tyre model, the effect of the \(p\) inflation pressure vanished. The importance of the \(C^{\prime}\) prime constant, characterising the \"flexibility\" of the tyre, was also strengthened by the finite element simulation. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{F (**kN**)} & \multirow{2}{*}{p (**kPa**)} & \multicolumn{3}{c}{**Complex Tyre FEM Model**} & \multicolumn{3}{c}{**Simple Tyre FEM Model**} \\ \cline{3-8}  & & \(q_{max}\) (**kPa**) & \(q_{avg}\) (**kPa**) & **Proportion (-)** & \(q_{max}\) (**kPa**) & \(q_{avg}\) (**kPa**) & **Proportion (-)** \\ \hline
17.5 & 430 & 801 & 391 & 2.0 & 1464 & 717 & 2.0 \\ \hline
20.0 & 430 & 996 & 414 & 2.4 & 1466 & 700 & 2.1 \\ \hline
22.5 & 430 & 1192 & 431 & 2.8 & 1475 & 696 & 2.1 \\ \hline
20.0 & 530 & 788 & 441 & 1.8 & 1527 & 730 & 2.1 \\ \hline
22.5 & 530 & 932 & 469 & 2.0 & 1549 & 720 & 2.2 \\ \hline
25.0 & 530 & 1104 & 471 & 2.3 & 1563 & 729 & 2.1 \\ \hline
22.5 & 630 & 932 & 469 & 2.0 & 1608 & 736 & 2.2 \\ \hline
25.0 & 630 & 918 & 516 & 1.8 & 1637 & 747 & 2.2 \\ \hline
27.5 & 630 & 1031 & 511 & 2.0 & 1651 & 769 & 2.1 \\ \hline
25.0 & 730 & 940 & 531 & 1.8 & 1696 & 759 & 2.2 \\ \hline
27.5 & 730 & 971 & 560 & 1.7 & 1722 & 782 & 2.2 \\ \hline
30.0 & 730 & 1036 & 557 & 1.9 & 1736 & 816 & 2.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of the tyre–pavement interaction simulations. Considering the fact that tyre manufacturers provide values of allowable inflation pressure and wheel load for operation, Equations (7) and (8) can be further simplified (Figure 11b). The connection between the allowable wheel load and the inflation pressure of the tyre can be described by a linear function, according to the manufacturers' data (R\({}^{2}\) = 0.99):  
\[F=0.0248p+6.30. \tag{9}\]  
Substituting Equation (9) into Equations (7) and (8), the connection between the average contact pressure under operational conditions and the inflation pressure can be described as follows:  
1. In case of the complex tyre model, \[q=0.449p+197.45.\] (10)
2. In case of the simplified tyre model, \[q=0.000174p^{2}+0.1378p+569.38\approx 0.334p+512.57.\] (11)  
Applying Equations (10) and (11), the average contact pressure \(q\) on the pavement surface can be estimated from the inflation pressure of the tyre \(p\). The author of [11], in his original paper, analysed the tyres of various manufacturers, i.e., Michelin, Firestone, Goodyear, and General, and, by averaging laboratory test results, obtained a linear connection (see Table 1) similar to that obtained in our research study. By plotting and comparing the two linear model equations (Figure 11c), it can be seen that the result of the complex finite element tyre model is close to the laboratory results of the Goodyear and General tyres, which proves our results. On the contrary, the results of the simplified tyre model significantly differ. However, in the work of [28], it was stated that the model of [11], in the case of plain surface diagonal tyres, underestimated the contact stress; therefore, in that case, its use is not recommended. Since, by the shape of the contact area, the behaviour of the simplified tyre model was more similar to diagonal tyres, it was worth comparing it with the modified model equation, as recommended by [28]:  
\[q=0.723p+310. \tag{12}\]  
In this case, the similarity is better; consequently, the behaviour of the simplified tyre model also describes a real tyre type.