## 3 Results and Discussion
### Predictions of the Tyre Footprint Dimensions  
#### 3.2.1 FE-Simulation  
Once the coincidence of the FE model tyre flattening under load has been verified for all the considered pressure values, the focus moved on to other parameters of interest provided by the model. Figure 8 shows an example of the deformation of the FE model of the tyre in the direction of the vertical axis (\(z\)) for the inflation pressure of 1.0 bar and for both the tyres. The \(z\)-axis coincides with the application direction of the force vector, i.e., the \(z\)-axis is perpendicular to the support plane. As shown in the figure, the tyre deflection involves a large part of the tyre itself and its effects interest almost the entire carcass. The tyres selected during the experimentation are worn tyres, well representing real operating conditions, and the geometries shown in the FE model are close to reality. The 420/85 R24 tyre has less wear and, therefore, higher lugs; this gives a reinforcement of the contact area and, hence, a lower concavity in the central area of the tyre contact footprint. On the contrary, since the lugs of the 460/85 R34 tyre are more worn, the central area of the contact footprint is more concave. Figure 9 shows the 3D FE model of the contact pattern when the inflation pressure is 1.0 bar for both the tyres. The figures also show a graduated scale for measuring the contact area; in particular, the geometry of the contact mark can be approximated to an ellipse with the edges coinciding with the boundaries of the _green zone_ (coinciding with the flat zone of the tyre deformed by the static loads). For each case, a major _longitudinal axis_ (i.e., along the median plane of the tyre) and a minor _transversal axis_ of the contact area (i.e., along a plane containing the rotation axis of the tyre) were identified. In general, the dimensions of the contact marks of the 420/85 R24 tyre reach about 675 mm  
Figure 8: 3D FEM vertical deformations in direction of compression load i.e., for 420/85 R24 (**a**) and 460/85 R34 (**b**) at the inflation pressure of 1.0 bar. for the longitudinal axis and 575 mm for the transversal axis, whilst for the 460/85 R34 tyre they are about 935 mm for the longitudinal axis and 558 mm for the transversal axis. The dimensions comply with the measurements made on the actual tyre during the compression test and are in accordance with the dimensions obtained from simulations and literature formulas [52]. Indeed, the size of the longitudinal axis of the contact pattern coincides with the size of the tyre semi-diameter in the absence of deformation. In addition, the contact pattern for both the tyres does not vary much when the inflation pressure varies. The dimensions of the contact marks in correspondence with different values for Young's modulus and Poisson's ratio were then analysed, and the results of these comparisons on the different lengths of the contact marks are reported as a function of the two cited coefficients in Figure 10 (for readability only the results at the pressure of 1.0 bar are reported; the trend and the conclusions relevant to the other pressure setting are similar). In those figures, the longitudinal and transversal dimensions of the FEM footprint axis of the 420/85 R24 tyre with different equivalent Young's moduli (\(E\)) and Poisson's ratios (\(\
u\)) are represented.