# Two-Lane Highways Crest Curve Design. The Case Study of Italian Guidelines
## 2 The Overtaking Maneuver and the Passing Sight Distance (PSD)
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model Name or Country** & **Relationships** \\ \hline Italy [10] & \(\mathrm{PSD}=5.5\) V \\ \hline Switzerland [23] & \(\mathrm{PSD}=6.7\) V \\ \hline France [24] & \(\mathrm{PSD}=550\) [m] \\ \hline  & \(\mathrm{PSD}=\mathrm{d}_{5}+\mathrm{PSD}_{\mathrm{c}}\) \\  & \(\mathrm{d}_{5}=\mathrm{G}_{1}^{\mathrm{N}}+1.47\mathrm{t}_{5}+\Delta_{\mathrm{c}}\) \\  & \(\mathrm{PSD_{c}}=1.47(2\mathrm{V}_{1}+\mathrm{m})\mathrm{t}_{6}+\mathrm{d}_{3}\) \\ [PERSON] model [25] & \(\mathrm{t}_{6}=0.68\big{[}\frac{\mathrm{G}_{1}+\Delta_{\mathrm{c}}}{2}\big{]} \big{.}+\big{(}\frac{1.47\mathrm{m}}{2\mathrm{a}}\big{)}\) \\  & \(\Delta_{\mathrm{c}}=\mathrm{G}_{1}-1.47\mathrm{m}\mathrm{t}_{6}\) \\  & \(\mathrm{a}=\mathrm{a}_{\mathrm{max}}\Big{[}1-\frac{\mathrm{V}_{1}+\frac{\mathrm{ m}}{2}}{\mathrm{V}_{\mathrm{max}}}\Big{]}\) \\ \hline  & \(\mathrm{PSD}=2\mathrm{V}_{\mathrm{d}}\Big{(}2.93+\frac{\mathrm{L}_{\mathrm{p}} -\Delta_{\mathrm{c}}}{\mathrm{m}}\Big{)}\) \\ Glennon model [26] & \(\Delta_{\mathrm{c}}=\mathrm{L}_{\mathrm{p}}+1.47\mathrm{m}\bigg{\{}\frac{\big{(} 2.93+\mathrm{L}_{\mathrm{c}}+\mathrm{L}_{\mathrm{p}}\big{)}}{1.47(2\mathrm{V} _{\mathrm{d}}-\mathrm{m})}-\Big{[}\frac{5.8\mathrm{V}_{\mathrm{d}}\big{(}2.93 \mathrm{m}+\mathrm{L}_{\mathrm{c}}+\mathrm{L}_{\mathrm{p}}\big{)}}{1.47\mathrm{ d}_{3}(2\mathrm{V}_{\mathrm{d}}-\mathrm{m})}\bigg{]}^{\frac{1}{2}}\bigg{\}}\) \\ \hline  & \(\mathrm{PSD_{c}}=2.93\mathrm{V}_{\mathrm{d}}\big{(}\mathrm{t}_{6}+\mathrm{h} \big{)}\) \\  & \(\mathrm{t}_{6}=\mathrm{p}_{\mathrm{a}}+\mathrm{t}_{\mathrm{a}}-\frac{\mathrm{d} _{\mathrm{d}}\mathrm{t}_{6}}{5.58\mathrm{V}_{\mathrm{d}}}\big{(}\mathrm{t}_{ \mathrm{a}}+2\mathrm{h}\big{)}\) \\  & \(\mathrm{t}_{\mathrm{a}}=-\mathrm{h}+\sqrt{\frac{\mathrm{h}^{2}+5.88\mathrm{V}_{ \mathrm{d}}}{2}[\mathrm{t}_{\mathrm{p}}+\mathrm{L}_{\mathrm{c}}+1.4\mathrm{h}(2 \mathrm{V}_{\mathrm{d}}-\mathrm{m})]}{1.47\mathrm{d}_{3}(2\mathrm{V}_{\mathrm{ d}}-\mathrm{m})}\) \\ [PERSON] et al. Model [27] & \(\Delta_{\mathrm{c}}=\mathrm{L}_{\mathrm{p}}+1.47(\mathrm{V}_{\mathrm{d}}- \mathrm{m})\mathrm{h}-1.47\mathrm{mt}_{6}\) \\  & \(\mathrm{PSD_{c}}=2.93\mathrm{V}_{\mathrm{d}}\Big{(}\mathrm{t}_{6}^{\mathrm{c}}+ \mathrm{h}\Big{)}\) \\  & \(\mathrm{t}_{6}^{\mathrm{c}}=\frac{1.47(\mathrm{V}_{\mathrm{d}}-\mathrm{m}) \mathrm{h}+\mathrm{L}_{\mathrm{p}}}{1.47\mathrm{m}}\) \\  & \(\mathrm{PSD_{c}}=2.93\mathrm{V}_{\mathrm{d}}\big{(}\mathrm{t}_{6}+\mathrm{h} \big{)}\)\(\Delta_{\mathrm{c}}\leq 0\) \\  & \(\mathrm{PSD_{c}}=2.93\mathrm{V}_{\mathrm{d}}\Big{(}\mathrm{t}_{6}^{\mathrm{c}}+ \mathrm{h}\big{)}\)\(\Delta_{\mathrm{c}}\geq 0\) \\ \hline  & \(\mathrm{PSD}=230\) m for V = 50 km/h \\ [PERSON] and [PERSON] model [28] & \(\mathrm{PSD}=365\) m for V = 70 km/h \\  & \(\mathrm{PSD}=575\) m for V = 110 km/h \\ \hline  & \(\mathrm{PSD_{complete}}=1.47\mathrm{V}_{\mathrm{crit}}\mathrm{t}_{5}+\frac{1.47 \mathrm{a}_{1}^{2}}{2}+1.47\mathrm{V}_{\mathrm{d}}\mathrm{t}_{6}\mathrm{d}_{3}\) \\ [PERSON] et al. model [29] & \(\mathrm{PSD_{short}}=1.47\mathrm{V}_{\mathrm{crit}}\mathrm{p}_{\mathrm{a}}+1.47 \mathrm{V}_{\mathrm{crit}}\mathrm{t}_{8}-\frac{1.47\mathrm{d}_{5}^{2}}{2}+ 1.47\mathrm{V}_{\mathrm{min}}\mathrm{t}_{9}+\mathrm{d}_{3}+1.47\mathrm{V}_{ \mathrm{0}}\big{(}\mathrm{p}_{\mathrm{a}}+\mathrm{t}_{8}+\mathrm{t}_{9}\big{)}\) \\ \hline  & \(\mathrm{PSD}=\mathrm{d}_{1}+\mathrm{d}_{2}+\mathrm{d}_{3}+\mathrm{d}_{4}\) \\  & \(\mathrm{d}_{1}=\frac{\mathrm{t}_{1}}{3.6}\Big{(}\mathrm{V}-\mathrm{m}-\frac{ \mathrm{a}\mathrm{t}_{1}}{2}\Big{)}\) \\ American Association of State Highway and & \(\mathrm{d}_{2}=\frac{\mathrm{t}_{3}}{3.6}\mathrm{V}_{2}\) \\ Transportation Officials-AASHTO Green Book [30] & \(\mathrm{d}_{3}\leq\mathrm{d}_{3}\leq 90\) m \\  & \(\mathrm{d}_{4}=\) 2/3 d\({}_{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Passing sight distance (PSD) models.