# The Effect of Speed Humps on Instantaneous Traffic Emissions
## 4 Results and Discussion
### The Impact of Speed Humps on \(\mathrm{CO_{2}}\) Emissions  
In Figures 7 and 8 we present the results of the computations on instant emissions of \(\mathrm{CO_{2}}\). The Figure 7 shows the \(\mathrm{CO_{2}}\) emissions as a function of density for different number of speed humps. The reported ranges go from 0.01 to 1.0 for \(\rho\), and from 0 g/s to 35 g/s for \(\mathrm{CO_{2}}\). We observe that the maximum emission values are in the range from 30 g/s to 35 g/s for the studied cases, we also noticed three different phases. The first phase for \(0<\rho\leq 0.12\) corresponds to the free-flow phase, as observed in Figure 4. In this phase, each test case shows a very low increase on \(\mathrm{CO_{2}}\) emissions. However, when comparing the initial \(\mathrm{CO_{2}}\) emission values of each studied case we found a significant difference, this comes from an increase in the stop-and-go effect due to the rise on the number of speed humps. After the first phase there is a very rapid increase on \(\mathrm{CO_{2}}\) emissions for the cases with 1, 3, 5 and 10 speed humps, and only a smooth increase for the cases with higher number of speed humps. This shows a high influence of speed humps on \(\mathrm{CO_{2}}\) emissions for the interval \(0.12<\rho\leq 0.48\). Please note that all the test cases reached a peak on \(\mathrm{CO_{2}}\) emissions in this phase. The third phase for \(0.48<\rho\leq 1\) shows a steady fall on \(\mathrm{CO_{2}}\) emissions for all cases because of zero velocities due to traffic congestions. Observe that at this phase the curves of the \(\mathrm{CO_{2}}\) emission overlap, this suggest that speed humps have no significant effect on \(\mathrm{CO_{2}}\) emissions for \(\rho>0.48\). Observe that for all the cases, the \(\mathrm{CO_{2}}\) emission converge to the \(f_{1}\) value from Table 2 as we increase the density, thus vehicles have zero velocity. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Pollutant** & **Vehicle Type** & \(E_{0}\) & \(f_{1}\) & \(f_{2}\) & \(f_{3}\) & \(f_{4}\) & \(f_{5}\) & \(f_{6}\) \\ \hline \(\mathrm{CO_{2}}\) & Petrol car & 0 & 5.53 \(\times 10^{-1}\) & 1.61 \(\times 10^{-1}\) & \(-2.89\times 10^{-3}\) & 2.66 \(\times 10^{-1}\) & 5.11 \(\times 10^{-1}\) & 1.83 \(\times 10^{-1}\) \\ \(\mathrm{NO_{2}}\) & Petrol car (\(a\geq-0.5\,\mathrm{m/s^{2}}\)) & 0 & 6.19 \(\times 10^{-4}\) & 8.00 \(\times 10^{-5}\) & \(-4.03\times 10^{-6}\) & \(-4.13\times 10^{-4}\) & 3.80 \(\times 10^{-4}\) & 1.77 \(\times 10^{-4}\) \\ \(\mathrm{NO_{2}}\) & Petrol car (\(a<-0.5\,\mathrm{m/s^{2}}\)) & 0 & 2.17 \(\times 10^{-4}\) & 0 & 0 & 0 & 0 & 0 \\ \(\mathrm{VOC}\) & Petrol car (\(a\geq-0.5\,\mathrm{m/s^{2}}\)) & 0 & 4.47 \(\times 10^{-3}\) & 7.32 \(\times 10^{-7}\) & -2.87 \(\times 10^{-8}\) & -3.41 \(\times 10^{-6}\) & 4.94 \(\times 10^{-6}\) & 1.66 \(\times 10^{-6}\) \\ \(\mathrm{VOC}\) & Petrol car (\(a<-0.5\,\mathrm{m/s^{2}}\)) & 0 & 2.63 \(\times 10^{-3}\) & 0 & 0 & 0 & 0 & 0 \\ \(\mathrm{PM}\) & Petrol car & 0 & 0 & 1.57 \(\times 10^{-5}\) & \(-9.21\times 10^{-7}\) & 0 & 3.75 \(\times 10^{-5}\) & 1.89 \(\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Emission functions values; \(a\) is the acceleration of a vehicle; selected and reproduced from [51]. Figure 6: Time–space diagrams and different densities of vehicles. To study the effect of many speed humps we performed simulations with more than 30 speed humps, in Figure 8 we show CO\({}_{2}\) emissions as a function of speed humps for different densities. We increased the number of speed humps from 0 to 100 with equidistant distribution. We took a density value in the range of the previously identified phases. For the first phase we took \(\rho=0.1\) where we observe a rising trend on CO\({}_{2}\) emissions as we add more speed humps to the lane.