## 4 Discussion  
In regards to Figure 9, in the post-processing phase, the authors assumed two design approaches: The first one complies with the Italian standards about geometrical rules to design roads [47], and the second one complies with the Italian driving code [48]. The first approach assumes that RPCs are routes across carriageways raised to the same level, or close to the same level, as the sidewalks that provide access to the pedestrian crossing. Therefore, they do not have traffic-calming purposes. Three conditions should be filled: The contact between any part of the reference vehicle and the pavement should be avoided, the ride comfort experienced by driver and passengers should be guaranteed limiting the vertical acceleration, and the stopping (for crest curves) and heading (for sag curves) sight distance should be verified. In order to avoid contact between vehicle and pavement, geometrical criteria are defined by [49] to design crest and sag vertical curves: The minimum vertical radius is 20 m (\(R_{vmin2}\)) and 40 m (\(R_{vmin1}\)), respectively. Therefore, the absolute value of the maximum value of the vertical acceleration over a crest is higher than that over a sag: It is because of the different value of the permitted minimum vertical radius (\(R_{vmin}\)). Given the same vehicle speed and the minimum permitted value of the vertical radius, the vertical acceleration over a crest is double than over a sag (Equation (2)). Given the two values of \(R_{vmin1}\) and \(R_{vmin2}\), for three values of \(h\) (i.e., 5, 10, and 15 cm), the values of the maximum \(i\) and \(L_{a}\), \(L_{e}\), \(L_{f}\) have been calculated according to Equations (2)-(8). \[L_{a,2}=L_{e,2}=R_{vmin2}\ i/100=20\ i/100\ (\text{crest curves}) \tag{2}\]  
\[L_{a,1}=L_{e,1}=R_{vmin1}\ i/100=40\ i/100\ (\text{sag curves}) \tag{3}\]  
\[h=L_{A}\frac{i}{100}=\left(\frac{L_{a,1}}{2}+\frac{L_{a,2}}{2}\right)\frac{i} {100}=L_{E}\frac{i}{100}=\left(\frac{L_{e,1}}{2}+\frac{L_{e,2}}{2}\right)\frac {i}{100} \tag{4}\]  
The total length of the RPC has been calculated according to Equation (4):  
\[L_{t}=L_{a}+L_{c}+L_{e}=L_{a}+L_{f}+L_{e}-L_{a,2} \tag{5}\]  
having the conditions given by Equations (5)-(7):  
\[L_{a}=L_{a,1}+L_{a,2}=L_{e}=L_{e,1}+L_{e,2} \tag{6}\]  
Figure 15: Correlation between \(h_{m}\) e and \(max\)\(a_{z}\). \[i = i_{a}\ =\ i_{e}\ =\ \sqrt{\frac{20000\ h}{R_{min1}+R_{min2}}} \tag{7}\] \[L_{c} = 4\ \mathrm{m} \tag{8}\]  
Table 5 lists the results. The obtained values give the longitudinal profiles in Figure 16: According to the geometric criteria, the ramp slope increases with increasing \(h\). The results from the implementation of the proposed geometric criteria have been compared to each surveyed site: 29.2% of the sites satisfy the limits of \(i\) (i.e., site 1a, 1b, 2, 3, 4, 13, and 14). In order to satisfy the comfort ride criterion, given the maximum vertical acceleration (\(a_{elim}\)) laid down by [47], for three administrative speed limits (i.e., 20, 30 and 40 km/h) and three values of \(h\) (i.e., 5, 10, and 15 cm), the values of \(i\), \(R_{min}\), \(L_{a}\), and \(L_{e}\) (Figure 9) have been calculated according to Equations (2)-(8) and Equation (9):  
\[R_{min}=v^{2}/(12.96\times a_{elim}) \tag{9}\]  
where \(v\) is the administrative speed limit and \(a_{elim}\) is equal to 0.6 m/s\({}^{2}\). Table 6 lists the geometric characteristics of RPCs according to the comfort criterion. The values in Table 6 give the longitudinal profiles in \[L_{a,1}=L_{e,1}=R_{vmin1}\ i/100=40\ i/100\ (\text{sag curves}) \tag{3}\]0  
The longitudinal profiles in Figure 17 reveal that:  
* For a given value of \(h\), the comfort reasons imply longer RPCs than geometrical constrains (i.e., for \(h\) = 15 cm \(L_{t}\) ranges between 15.11 m and 31.78 m according to the comfort criterion, while \(L_{t}\) is 12.49 m according to the geometrical criterion).