## 3 Results and Discussion
### Predictions of the Tyre Footprint Dimensions
#### 3.2.2 Experimental Data Processing
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F Value** & \(p\)**-Value Prob \textgreater{} F** \\ \hline Model & 3650.52 & 4 & 912.63 & 20.80 & \textless{}0.0001 \\ _A-Pressure_ & _2.59_ & \(1\) & _2.59_ & _0.059_ & _0.8102_ \\ _B-E_ & _0.31_ & \(1\) & _0.31_ & _7.018E\textless{}003_ & _0.9339_ \\ _C-\(\
u\)_ & _1507.54_ & \(1\) & _1507.54_ & _34.35_ & \textless{}0.0001 \\ _D-Type_ & _76.75_ & \(1\) & _76.75_ & _1.75_ & _0.1980_ \\ Residual & 1097.12 & 25 & 43.88 & & \\ Cor Total & 4747.64 & 29 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ANOVA on the values of the transversal dimension of the tyre footprint referred to the four possible factors of influence. Figure 11: 3D representation of the interpolation models for the footprint longitudinal axis of the two tested tyres (**a**: 420/85 R24; **b**: 460/85 R34) as a function of Poisson’s ratio and tyre inflating pressure. in Figures 12 and 13; it is composed by two equations (\(\
u\): equivalent Poisson's ratio) which differ depending on the tyre type (adjusted R\({}^{2}\) = 0.96):  
\[\left\{ \begin{array}{l}420/85\;\text{R24}:T\;axis=-2958.4+15636.6\cdot\
u-1724 7.7\cdot\
u^{2}\\ 460/85\;\text{R34}:T\;axis=-3253.4+16217.5\cdot\
u-17247.7\cdot\
u^{2}\\ \end{array} \right. \tag{3}\]  
In this case, the analysis proposed a quadratic model as being most appropriate for the fitting (the linear model presented an adjusted R\({}^{2}\) = 0.85). Figure 12: 2D representation of the interpolation models for the footprint transversal axis of the two tested tyres (black line: 420/85 R24; red line: 460/85 R34) as a function of Poisson’s ratio and at three tyre-inflating pressures: (**a**) 1.0 bar; (**b**) 1.3 bar; (**c**) 1.6 bar. FEM results are also represented in the pictures as round points. Figure 13: 3D representation of the interpolation models for the footprint transversal axis of the two tested tyres (**a**: 420/85 R24; **b**: 460/85 R34) as a function of Poisson’s ratio and the tyre-inflating pressure. As visible from Equation (3) and the graphs, the effect of an increase in Poisson's ratio toward the value of 0.50 (i.e., a perfectly incompressible solid) is slightly different for the two tyres:  
* for the smaller one (420/85 R24), an increase in Poisson's ratio shortens monotonically (but non linearly) the transversal dimension of the tyre footprint, thus showing an opposite behaviour as compared to the other dimension;
* for the bigger one (460/85 R34), after a very small increase until the value of 0.475, a further increase in the Poisson's ratio has the effect of shortening the transversal dimension of the tyre footprint. The type of tyre has an influence only on the value of the transversal dimension of the tyre footprint at a Poisson's ratio of 0.46, i.e., in determining a different vertical starting point of the graphs in a Cartesian plane (Figure 12) or space (Figure 13); instead, the difference between the values reached by the two tyres in correspondence to a Poisson's ratio of 0.50 is very small (about 6 mm).