# Exploring the Feasibility of Autonomous Lighting Systems for Pedestrian Crossings in Off-Grid Areas
## 2 Materials and Methods  
### Lighting Formal Requirements  
In the current Polish law regulations [11; 36; 37], the illumination of pedestrian crossings located outside illuminated areas should be realized by means of a dedicated lighting solution, used jointly with transition zones to ensure the driver's eyesight is properly adapted to the night conditions. The luminaires in use at pedestrian crossings are characterized by the double asymmetry of the light beam. Figure 2 shows an example of the light distribution curve of dedicated luminaires used to illuminate pedestrian crossings. On a typical single carriageway, two-lane road with one lane in each direction, two luminaires are installed individually for each direction, in the arrangement presented in Figure 3.  
By adhering to the specified requirements in terms of beam distribution, installation geometry and required lighting parameters, it is possible to realize pedestrian silhouette lighting in positive contrast [11]. The required illuminance parameters at pedestrian crossing with asymmetrical light distribution luminaries for carriageways illuminated in Class C are defined in Table 1.  
The quantitative requirements for the lighting performed at the pedestrian crossing corresponding to the requirements in Table 1 refer to the measuring points located at the pedestrian crossing in the following planes: vertical (Figure 4) and horizontal (Figure 5) and control points (A, B, C, D, E, F). Points 31 \(\div\) 40, 51 \(\div\) 60, 71 \(\div\) 80 denote the locations for measuring the luminous intensities in the vertical plane Ev for the first direction of observation. Points 41 \(\div\) 50, 61 \(\div\) 70, 81 \(\div\) 90 denote the locations for measuring the luminous intensities in the vertical plane Ev for the second direction of observation. qwPoints A, B, C, E, F are the extreme pedestrian crossing points for which luminous intensities measurements in the vertical plane Ev at a height of 1 m need to be conducted for each direction of traffic. Points 1 \(\div\) 30 denote the locations for measuring the luminous intensities in the horizontal plane [Eh] at the pedestrian crossing. Figure 3: Location of dedicated luminaires in relation to geometry of the pedestrian crossing. Figure 2: Example of light distribution curve of dedicated luminaire used to illuminate pedestrian crossings. A pedestrian crossing located in an unlit area requires a transition zone with a length proportional to the speed limit at the pedestrian crossing. Usage of the transition zone ensures that the right conditions for the driver's right-vision adaptation are created. The speed limit for pedestrian crossings is 70 km/h. Therefore, the length of the transition zone is 100 m behind the illuminated pedestrian crossing (Table 2). Figure 6 presents a diagram of the transition zone in the pedestrian crossing area, illuminated by a dedicated solution, together with an illustration of the principle of setting the level in classes PC and C3. According to the guidelines, the basic lighting level at \begin{table}
\begin{tabular}{c c c} \hline \hline
**Permissible Speed** & **Minimum Zone** & **Recommended Zone** \\ \(V_{\textit{dop}}\) [km/h] & **Length [m]** & **Length [m]** \\ \hline
30 & 42 & \\ \hline
40 & 56 & \\ \hline
50 & 70 & 100 \\ \hline
60 & 84 & \\ \hline
70 & 98 & \\ \hline
80 & 112 & \\ \hline
90 & 125 & 150 \\ \hline
100 & 139 & \\ \hline
110 & 153 & \\ \hline
120 & 167 & \\ \hline
130 & 181 & 200 \\ \hline
140 & 194 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Required length of the transition zone behind the pedestrian crossing [11]. Figure 5: Example of a grid for horizontal measurements of luminous intensity (Eh) at a pedestrian crossing. the pedestrian crossing is set to class PC 4 and can be changed according to accident risk analysis results [11]. Together with lighting installed at the pedestrian crossing, this condition creates a minimum 200 m of illuminated area.