# Two-Lane Highways Crest Curve Design. The Case Study of Italian Guidelines
## 2 The Overtaking Maneuver and the Passing Sight Distance (PSD)  
The overtaking maneuver is a key issue for two-lane highways, because it requires occupying the opposing lane, which represents a serious safety concern [6; 9; 12; 13]. Accidents occurred due to overtaking maneuvers represent around 38% of the total accidents on Italian two-lane highways [14]. Accident severity associated to overtaking maneuvers is usually higher than in other maneuver types [12; 13]. The overtaking maneuver's frequency depends on various factors, including traffic volumes, users' motivation, and their psychophysical state and highway alignment (vertical and horizontal) [15]. The traffic flow variable that considerably influences the propensity to do an overtake maneuver is the vehicular density k. In steady-state traffic condition [16; 17; 18], the density \(k\) can be estimated by knowing the flow rate q and the mean space speed v\({}_{\text{s}}\), with the well-known fundamental relations of traffic flow: k = q/v\({}_{\text{s}}\). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & & & & & & & & \\ \hline  & **40** & **50** & **60** & **70** & **80** & **90** & **100** & **110** & **120** & **130** & **140** \\ \hline  & & & & & & & & & & & \\ \hline Austria & 1500 & 2000 & 3000 & 4000 & 7500 & - & 12,500 & - & 20,000 & - & 35,000 \\ Belgium & - & - & 1600 & - & - & 7500 & - & - & 7824 & - & - \\ Denmark & - & - & - & - & 3500 & - & 6000 & - & 15,000 & - & - \\ Germany & & & & & & & & & & & \\ 1984 & - & - & 3750 & 3500 & 5000 & 7000 & 10,000 & - & 20,000 & - & - \\
1995 & - & 1400 & 2400 & 3150 & 4400 & 5700 & 8300 & - & 16,000 & - & - \\ New Research & - & - & 800 & 1500 & 2700 & 4700 & 7600 & - & 17,500 & - & - \\ France & 700 & - & 1500 & - & 3000 & - & 6000 & - & 12,000 & - & 18,000 \\ Italy & 500 & - & 1000 & - & 3000 & - & 7000 & - & 14,000 & - & - \\ The Netherlands & - & - & - & - & 1800 & - & 4100 & - & 12,400 & - & - \\ Spain & - & - & - & - & 3500 & - & 6000 & - & 12,000 & & \\ Sweden & - & 1100 & - & 3500 & - & 7000 & - & 10,000 & - & - & - \\ Sweden * & - & 600 * & - & 1800 * & 1800 * & - & - & - & - & - \\ Switzerland & 620 & 1500 & 2100 & 3000 & 4200 & - & 10,500 & - & 18,000 & - & 31,000 \\ United Kingdom & - & 1100 & 1900 & 3300 & 5900 & - & 10,500 & - & 18,000 & - & - \\ Canada & 400 & 700 & 1500 & 2200 & 3500 & 5500 & 7000 & 8500 & 10,500 & 12,000 & - \\ United States & 500 & 1000 & 1800 & 3100 & 4900 & 7100 & 10,500 & 15,100 & 20,200 & - & - \\ South Africa & 600 & - & 2000 & - & 5000 & - & 10,000 & - & 20,000 & - & - \\ Australia & - & 540 & 920 & 1570 & 2400 & 4200 & 6300 & 9500 & 13,500 & 19,500 & - \\ Japan & - & 800 & 1400 & - & 3000 & - & 6500 & - & 11,000 & - & - \\ Greece & - & 1500 & 2500 & 3200 & 4300 & 5700 & 7400 & 11,000 & 15,000 & 20,000 & - \\ \hline \hline \end{tabular} Note.* Exceptional value.  
\end{table} 
Table 1: Minimum radii of crest vertical curves as a function of design speed in various countries (source [6]). As q increases for a given vehicle, the probability of encountering slow vehicles increases [19]. In other words, users have high probability to encounter slower vehicles and often are forced to queue up first and then overtake where the available sight distance D is greater than the passing sight distance PSD [19]. Consequently, the performance analyses of two-lane highways--whose objective is to determine the level of service (LOS) for an existing or proposed facility--include a specific evaluation of the percent time-spent-following [20]. Then, a PSD adequate for users to pass slow vehicles should be provided at frequent intervals on two-lane highways. In order to guarantee acceptable LOS, several highway design guidelines require a minimum percentage of passing zones in each direction of travel (e.g., 20% in Italy [10]). To ensure suitable safety conditions, overtaking is only allowed in the zones where available sight distance is higher than the required overtaking passing sight distance PSD [12; 21].