# Two-Lane Highways Crest Curve Design. The Case Study of Italian Guidelines
## 3 Analytical Derivation of Crest Curve Minimum Radius
### Case in Which \(D>L\)
#### Minimum Values of \(R_{v}\)  
Figure 6 shows \(\mathrm{R_{v}}\) values according to the Equations (17) and (28) obtained for \(\mathrm{h_{1}}=1.10\) m and \(\mathrm{h_{2(15)}}=1.39\) m. Similarly, Figure 7 shows \(\mathrm{R_{v}}\) values according to the Equations (17) and (28) obtained  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Country**} & \multicolumn{2}{c}{**Driver Eye Height [m]**} \\ \cline{2-4}  & \multicolumn{2}{c}{**Passenger Car**} & **Truck** \\ \hline Australia & 1.15 & 1.80 \\ \hline Austria & 1.00 & - \\ \hline France & 1.00 & - \\ \hline Germany & 1.00 & 2.50 \\ \hline Greece & 1.10 & - \\ \hline Japan & 1.20 & 1.50 \\ \hline South Africa & 1.05 & 1.80 \\ \hline Sweden & 1.10 & - \\ \hline Switzerland & 1.00 & 2.50 \\ \hline United Kingdom & 1.05 & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Driver’s eye height \(\mathrm{h_{1}}\) adopted in some countries.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**N.**} & \multirow{2}{*}{**Brand**} & \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Number of Vehicles Registered**} & \multicolumn{2}{c}{**Overall Height**} \\  & & & & **(Year 2006)** & **h [mm]** \\ \hline
1 & Fiat & Seicento & 1.1I & 480,518 & 1430 \\ \hline
2 & Fiat & Panda & 900 IE & 466,607 & 1440 \\ \hline
3 & Fiat & Uno & 45 3P & 448,715 & 1430 \\ \hline
4 & Lancia & Y & 1.2I & 439,421 & 1440 \\ \hline
5 & Fiat & Pinto & 55 3P & 438,184 & 1480 \\ \hline
6 & Fiat & 500 & L & 381,766 & 1330 \\ \hline
7 & ford & Ka & 1.3 & 232,805 & 1370 \\ \hline
8 & Renault & Clio & 1.1I 3P & 223,814 & 1420 \\ \hline
9 & Renault & Twingo & 1.2 & 222,087 & 1420 \\ \hline
10 & Fiat & Panda & 1.2 & 222,035 & 1540 \\ \hline
11 & Opel & Corsa & 1.0I 12V 3P & 219,870 & 1440 \\ \hline
12 & Autobianchi & Y10 & Fire & 175,018 & 1430 \\ \hline
13 & Ford & Focus & 1.8 TDDI SP & 167,753 & 1500 \\ \hline
14 & Toyota & Yaris & 1.0I 16V 3P & 157,158 & 1530 \\ \hline
15 & Volkswagen & Golf & 1.9 TDI Variant & 126,521 & 1490 \\ \hline
16 & Peugeot & 206 & 1.4 & 120,518 & 1430 \\ \hline
17 & Nissan & Mica & 1.0 CAT & 116,472 & 1540 \\ \hline
18 & Alfa Romeo & 147 & 1.9 JTD & 113,463 & 1440 \\ \hline
19 & Fiat & Tipo & 1.4 SP & 109,294 & 1450 \\ \hline
20 & Renault & Megane & 1.9 DCI Scenic & 107,323 & 1620 \\ \hline... &... &... &... &... &... \\ \hline
115 & Honda & Jazz & 1.2I DSI & 20,314 & 1530 \\ \hline  & - & - & TOTAL & 9,154,262 &... \\ \hline \hline \end{tabular}
\end{table}
Table 3: Top 20 car models registered in Italy listed by number of vehicles sold.  
for h\({}_{1}\) = 1.10 m and h\({}_{2(\rm{m})}\) = 1.48 m. In both cases, each curve R\({}_{\rm{v}}\)(\(\Delta\)i) reaches a maximum value R\({}_{\rm{v}}\)* for \(\Delta\)i = \(\Delta\)i *; instead, for \(\Delta\)i > \(\Delta\)i *, it results in R\({}_{\rm{v}}\) = R\({}_{\rm{v}}\)*. As can be observed from Figure 8, the differences \(\Delta\)R\({}_{\rm{v}}\) between R\({}_{\rm{v}}\) values calculated in the two scenarios (h\({}_{2(15)}\) = 1.39 m and h\({}_{2(\rm{m})}\) = 1.48 m) increase with increasing PSD. Finally, Figures 9 and 10 show the differences (\(\Delta\)R\({}_{\rm{v}}\)) between the vertical radii calculated with the Italian model (h\({}_{2}\) = 1.10 m) and the values obtained, respectively, for h\({}_{2(\rm{m})}\) = 1.48 m and h\({}_{2(15)}\) = 1.39 m. It should be noted that the deviations are up to 12%.