# ECOTIRE: A New Concept of a Smart and Sustainable Tire Based on a Removable Tread
## 3 Design Requirements for Casing-Tread Mechanical Connections
### Analysis of Parameter to Determine the Geometry of the Casing-Tread Mechanical Connection  
The preliminary dynamic study allowed us to propose various geometries that could be suitable, including grooved, chevron, pyramidal shapes, etc. Of this last proposal, the pyramidal geometry with a rhomboidal (diamond) base provides several notable benefits. Firstly, during the assembly and disassembly of the tread, this geometry offers enhanced stability and alignment, making the process more efficient and reliable. Additionally, the unique shape of the rhomboidal base facilitates a secure fit, reducing the likelihood of slippage or misalignment over time. Moreover, in terms of force transmission during operation, this geometry excels due to its ability to evenly distribute mechanical stresses across the tread surface. The pyramidal structure effectively distributes forces, minimizing tire wear and improving overall performance and longevity. Overall, the combination of stability, alignment, and efficient force transmission makes the pyramidal geometry with a rhomboidal base an attractive choice for the mechanical connection. More specifically, the geometry depicted in Figure 4 was thoroughly analyzed. This figure showcases the characteristic dimensions and angles currently under study to optimize the union. By closely examining these dimensions and angles, the goal is to refine the design further and maximize its effectiveness in enhancing tread assembly, disassembly, and force transmission. Figure 4: Representation of the main parameters for proposed geometric optimization of the casing–tread connection and forces transmission through rhomboidal base geometry (top and side views, respectively). The casing is represented in gray, and the tread is shown in green. Figure 4 presents top view and a side view of the truncated pyramid, which is defined based on the major diagonal length D, and two characteristic angles, \(\beta\) and \(\gamma\). For its part, the slope of the walls of the truncated pyramid has been characterized with an angle \(\alpha\), as can also be seen in Figure 4. Considering the general use of the tire being designed, no reason has been identified to propose asymmetric geometries, so the geometries have been created symmetrical with respect to the OX and OY axes. From this symmetry and knowing that the sum of the four angles of the rhombus must be 360\({}^{\circ}\), to define it geometrically, it is enough to determine the major diagonal and only one of the angles of the base of the pyramid, \(\beta\) and \(\gamma\). The proposed final geometry only depends on D, \(\beta\), and \(\alpha\). Additionally, it can be observed in Figure 4 that by applying longitudinal forces, Fx, and lateral forces, Fy, through this geometry, a component is obtained in the direction of sliding and another normal to the face of the pyramid. To maximize the transmitted force, the objective is to maximize the normal force, Fnx and Fny, and minimize the sliding force, Fs, as indicated in Equation (2). \[\text{F}_{\text{t}}=\sqrt{\text{F}_{\text{x}}{}^{2}+\text{F}_{\text{y}}{}^{2}} \Rightarrow\theta=\text{arcsin}\frac{\text{F}_{\text{y}}}{\text{F}_{\text{x} }}\Rightarrow\text{optimum}\rightarrow\theta=\beta\rightarrow\text{F}_{ \text{n}}=\text{F}_{\text{t}};\,\text{F}_{\text{d}}=0 \tag{2}\]  
From Equation (2), it is possible to consider the longitudinal and lateral grip values that apply to the tire and obtain a value of the angles \(\beta\) and \(\gamma\) optimized for said grip values, as expressed in Equations (3) and (4).