## 5 Parametric Sweep: Visualization and Analysis
\(0.71\lesssim\mu\lesssim 0.79\), \(\rho=218\;[m]\). \(\rho\) is the curvature parameter used, whether \(r\) or \(R\). Pavement conditions: dry, sandy. Sand particle mean diameter \(\sim\)10\({}^{3}\;[\mu m]\). In this figure, the percentage relative errors between models, having as a reference the rotated cylindrical/curvature radius (that is presented in Equation (14)), vary between \(0\leq\%E\leq 4.47\). Figure 9: Maximum velocity vs. super-elevation angle. \(18\lesssim\rho\lesssim 418\;[m]\), \(\mu=0.75\). \(\rho\) is the curvature parameter used, whether \(r\) or \(R\). Pavement conditions: dry, sandy. Sand particles mean diameter \(\sim\)10\({}^{3}\;[\mu m]\). In this figure, the percentage relative errors between models, having as a reference the rotated cylindrical/curvature radius one (that presented in Equation (14)), vary between \(0\leq\%E\leq 4.47\)  
Figure 11: Maximum velocity vs. super-elevation angle. \(18\lesssim\rho\lesssim 418\)\([m]\), \(\mu=0.165\). \(\rho\) is the curvature parameter used, whether \(r\) or \(R\). Pavement conditions: icy, no sand. In this figure, the percentage relative errors between models, having as a reference the rotated cylindrical/curvature radius (that is presented in Equation (14)), vary between \(0\leq\%E\leq 1.15\). Figure 12: Maximum velocity vs. super-elevation angle. \(0.1\lesssim\mu=\lesssim 0.23\), \(\rho=218\)\([m]\). \(\rho\) is the curvature parameter used, whether \(r\) or \(R\). Pavement conditions: icy, no sand. In this figure, the percentage relative errors between models, having as a reference the rotated cylindrical/curvature radius (that is presented in Equation (14)), vary between \(0\leq\%E\leq 1.50\). The first thing to notice is that there are indeed differences between models over maximum speeds before tires/pavement slippage. That is interesting since this involves a model (Equation (2)) that has been used for many years and constitutes the basis for numerous national regulatory systems, scantly discussed in terms of fundamentals such as the ones brought up here. It is not claimed here that the model has been a liability _per-se._ However, this finding could represent an opportunity to work on the lack of discussion of principles about the geometrophysical parameters involved in the general problem, such as the concepts of curvature radius and (highway) super-elevation and, furthermore, about concepts such as vehicle trajectory in these kinds of applications. Another interesting feature of the results is that the smaller differences between models are found in the most slippery conditions, Cf. Figures 9-12. That is perhaps counter-intuitive since an icy pavement surface conveys edgy model conditioning. On the other hand, if icy pavement implies the smaller-in-value non-geometrophysical parameter under consideration (Cf. Table 3), the results appear reasonable. Indeed, a comparison of Figures 8-10 shows that the sequence of model differences continues to augment with increasing friction coefficient values (\(\overline{\eta}_{s}=0.61\), %\(E_{Max}=3.94\), and \(\overline{\eta}_{s}=0.75\), %\(E_{Max}=4.71\), respectively). Please Cf. Table 3 again. As explained in Section 3.2, it has been established that models leading to Equations (13) and (14) are mathematically equivalent to the model expressed in Equation (2), Cf. [25]. This equivalence allows for the utilization of the former (Equation (14)) as a reference for comparison. This finding is particularly interesting since, to the best of our knowledge, this specific topic has not been addressed in the existing literature. Of course, the broader subject of developing and applying point mass models regarding the main problem reviewed by this paper is known, as well as the recognition that the model represented by Equation (2) is derived from practical approximation considerations applied to the model proposed by Equation (1), as explained in earlier sections. However, a quantitative analysis of this relationship and its derived consequences, as proposed in this study, has not been previously conducted.