# Analysis of the Efficiency of Slope Evacuation for Dense Crowds in Urban Street-Type Public Spaces
## 5 Results  
### Effect of Slope on Evacuation Time  
Evacuation simulations were conducted separately with an initial crowd density of 0.50 to 2.00 pedestrians/m\({}^{2}\) (with a step size of 0.50 pedestrians/m\({}^{2}\)), without considering road obstacles or any human intervention. Due to the randomness of the simulation results, in order to reduce the error, we performed three simulations for each slope and took the average value to draw a line graph of the change in evacuation time under different slopes, as shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Type of Mobility Impairment** & \multicolumn{8}{c}{**Percentage with Disabilities (\%)**} \\ \hline Unassisted walking using a wheelchair & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 & 100 \\ Unassisted walking using a cane & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 & 100 \\ Visually impaired & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 & 100 \\ Hearing impaired & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The types and percentages of disabled pedestrians in the evacuated crowd. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group Size** & **Working Condition** & **Group Type** & **Working Condition** & **Group Type** \\ \hline Group of 2 & 1 & O-O & 2 & M-M \\ \hline Group of 2 & 3 & O-M & 4 & O-J \\  & 5 & M-J & 6 & J-J \\ \hline \hline \multirow{4}{*}{Group of 3} & 7 & O-O-O & 8 & M-M-M \\  & 9 & O-O-M & 10 & O-M-M \\ \cline{1-1} Group of 3 & 11 & O-O-J & 12 & O-M-J \\ \cline{1-1}  & 13 & M-M-J & 14 & O-J-J \\ \cline{1-1}  & 15 & M-J-J & 16 & J-J-J \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Types of Different Groups. The total evacuation time of the crowd at different densities showed a fluctuating upward trend as the slope increased. In Figure 7, the slope time curves at different crowd densities have obvious inflection points at 4\({}^{\circ}\) and 8\({}^{\circ}\), which means that the evacuation efficiency of pedestrians increases rather than decreases at this slope. The reasons for this phenomenon include both individual and group factors:  
1. In terms of personal factors, on nearly horizontal ramps with a slope of less than 4\({}^{\circ}\), pedestrians' speed of movement increases to some extent due to the effect of gravity during the descent. However, on gently inclined ramps with a slope of more than 4\({}^{\circ}\), pedestrians will reduce their speed to maintain their stability to prevent falling due to the increased perception of the slope by the human body itself;
2. In terms of group factors, at a steeper 8\({}^{\circ}\) slope, especially in emergencies, evacuating crowds tend to step faster unconsciously and are more motivated to evacuate. Crowds tend to be closer to each other when evacuating, and the phenomenon of pedestrians pushing each other will be strengthened, which requires pedestrians to exert more physical strength and attention to maintain their balance. To a certain extent, this will increase the risk of stampede accidents. Slope landings place more stress on the knee joint than horizontal landings. As the slope increases, so does the risk of knee injury. Taken together, 4\({}^{\circ}\) is the ideal slope for different population densities. At this slope, pedestrians can maintain the continuity of pedestrian flow while avoiding the blockage and stoppage caused by the steep slope, reducing the time lost due to congestion. The 4\({}^{\circ}\) slope is also relatively easier to walk on and control for people of different ages and physical conditions, such as the elderly and children. Figure 7: Effect of slope on evacuation time at different densities: (**A**) The crowd density is 0.50 pedestrians/m\({}^{2}\); (**B**) The crowd density is 1.00 pedestrians/m\({}^{2}\); (**C**) The crowd density is 1.50 pedestrians/m\({}^{2}\); (**D**) The crowd density is 2.00 pedestrians/m\({}^{2}\).