# Type-Road Heat Transfer Coefficient Equation Proposal
## 7 Conclusions  
The current paper proposes a novel, physics-based equation that serves the purpose of computing, in real-time, the dynamic tyre-road heat transfer coefficient \(Hc\). This coefficient estimation relies on essential tyre compound characteristics and two dynamic parameters: the rolling speed of the tyre and the length of its footprint on the road. The work is motivated by the need to address a research question that has long been overlooked in this field: the lack of knowledge about the heat transfer coefficient between the tyre and the road. Despite its significant impact on the results generated by more intricate thermomechanical tire models, this parameter has historically been treated as a constant, even though the few values available in the literature exhibit significant variability, varying by more than one order of magnitude. This inconsistency has cast doubt on the suitability of these values for integration into advanced tyre models whose aim is to provide the most realistic results possible. The equation presented in this paper was developed considering the mechanism of heat transfer that occurs between the ground and the first layer of the rubber composing the tyre tread. This heat transfer predominantly occurs within the tyre surface layer, specifically through the contact area. The formulation of \(Hc\) is based on the average heat flux exchanged between the tyre surface and the ground throughout a full revolution of the wheel. To validate the proposed equation, comparisons with the values actually available in the existing literature were made. The results consistently demonstrated a close alignment with the empirical data. For instance, at high speeds of approximately 41.6 m/s (equivalent to 150 km/h) and a tire footprint length of 0.14 m, the proposed model provides a value of 1.22 \(\times\) 10\({}^{4}\) W/(m\({}^{2}\)K). Conversely, at lower speeds of 2.7 m/s (equivalent to 10 km/h), the equation yields a value of 3.1 \(\times\) 10\({}^{3}\) W/(m\({}^{2}\)K). These results support the theoretical justification for employing the empirical values that are commonly found in the literature. Upon careful analysis of the equation outcomes and thorough consideration of the underlying physics, it becomes evident that \(Hc\) is not a constant throughout the entire spectrum of vehicle speeds. Specifically, this work emphasises that the most widely used value of \(Hc\), which stands at 1.2 \(\times\) 10\({}^{4}\) W/(m\({}^{2}\)K), is most suitable within the medium- to high-speed range, spanning from 100 km/h to 200 km/h, with the tire footprint length set at 0.14 m. However, when vehicle speeds fall within the 10 km/h to 50 km/h range, it is more fitting to halve the aforementioned \(Hc\) value. For higher speeds, employing the widely disseminated \(Hc\) value could potentially lead to an underestimation of the actual heat exchanged with the ground. An additional advantage of the formula Is Its simplicity and efficiency. It entails minimal computational overheads and can be seamlessly integrated into more complex tyre models, adding the needed real-time characterisation of the heat exchange between the tyreand the ground. This integration serves to refine the prediction of tyre behaviour, fostering smarter tyre design and utilisation that can effectively mitigate tyre-related pollution. Looking ahead, this research will expand to encompass the validation of the equation using experimental data gathered from real vehicles operating at various speeds. Moreover, the aim is to incorporate the formula into a new comprehensive thermos-mechanical tyre model actually under development by the authors. Conceptualization, P.C., L.C. and A.M.; Methodology, P.C., L.C. and A.M.; Software, P.C. ; Validation, P.C. and L.C. ; Formal analysis, P.C. and A.M.; Investigation, P.C. and L.C. ; Resources, A.M.; Data curation, P.C. and L.C. ; Writing--original draft, P.C. and L.C. ; Writing--review & editing, P.C., L.C. and A.M.; Visualization, P.C.