# Numerical Assessment of Side-Wind Effects on a Bus in Urban Conditions
## 4 Discussion  
The low-cruising speed creates a substantial deviation in drag, which also reduces the accuracy of the drag loss calculation. In the symmetric flow cases, the largest deviation was \(\pm\)0.01, which corresponds to \(\pm\)10 counts. Due to the already low \(C_{D}\) value and the aerodynamically favourable geometry, further improvements to reduce the drag can be challenging with the existing methods [32]. It has to be noted that improvement below the deviation is considered to be an ineffective method. Side winds and drag connections are an often researched field. [PERSON] et al. [13] and [PERSON] et al. [6] showed that the drag increase at 41 m/s and 27 m/s resulted in around a  
Figure 12: Velocity distribution at (**a**) x = 12.5 m, (**b**) 13 m, and (**c**) 14 m y–z vertical sections. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Side-Wind Speed** & **10 km/h** & **15 km/h** & **20 km/h** \\ \hline symmetric & 0362 \(\pm\) 0.009 & 0.380 \(\pm\) 0.008 & 0.389 \(\pm\) 0.010 \\
1 m/s & 1.986 \(\pm\) 0.065 & 1.418 \(\pm\) 0.044 & 1.173 \(\pm\) 0.044 \\
1.5 m/s & 2.425 \(\pm\) 0.174 & 2.110 \(\pm\) 0.061 & 1.591 \(\pm\) 0.053 \\
2 m/s & 2.305 \(\pm\) 0.236 & 2.318 \(\pm\) 0.105 & 1.927 \(\pm\) 0.082 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Drag coefficients at different side-wind and cruising speed magnitudes. 10-15% change in the drag coefficient. Compared with the results of this study, their drag coefficients are relatively lower than the showcased results. However, the assumption is that, at lower cruising speeds (5.55 m/s), the low wind speed (2 m/s) has a higher impact on the flow field and the drag than at higher cruising speeds. The magnitude of the influence can be represented by velocity or drag coefficient triangles. When the bus travels at \(v_{c}\) cruising speed and is affected by a perpendicular side wind (\(v_{w}\)), the two vectors create a \(v_{T}\) total velocity. This method can also be applied to the drag coefficient. Since drag coefficients were attained first for the symmetrical flows, a connection was established. Using exponential fitting on three highly deviating values (see Table 5) could give extremely large freedom; in spite of this, Equation (3) (R\({}^{2}\) = 0.99) was defined. \[C_{DC}=0.0393\cdot ln(v_{c}\cdot 3.6\ \mathrm{s/m}) \tag{3}\]  
where \(C_{DC}\) is the drag coefficient at symmetrical flow. The next step was to evaluate the magnitude change due to the side wind. First to assess the difference between the \(C_{DT}\) and \(C_{DC}\) Equation (4) was used [33], to determine the magnitude of \(C_{DW}\) the wind-induced drag. \[C_{DT}=\sqrt{C_{DC}{}^{2}+C_{DW}{}^{2}} \tag{4}\]  
Second, the \(C_{DW}\) values were analysed and showed polynomial characteristics, with a regression of R\({}^{2}\) = 0.91. The relation of the perpendicular side wind and side-wind-induced drag can be expressed with the following Equation (5):  
\[C_{DW}=-0.4338\cdot v_{w}{}^{2}+1.9561\cdot v_{w}-0.0067 \tag{5}\]  
When the results of Equation (4) were compared with those of the average drag equation used by [PERSON] [34], Equation (4) showed better agreement in the low-speed zone. The wind-averaged drag in the previously mentioned study was only valid above 9 m/s, and as a result, it underpredicts the \(C_{DT}\) values, compared with the values of this study. It should be noted that the proposed Equations (3) and (5) are the most precise between 10 and 20 km/h. By applying Equations (3)-(5) to the driving cycle, the actual aerodynamic losses can be calculated when the bus is cruising. In addition, by knowing the drag coefficient, the aerodynamic power demand can also be calculated by using Equation (6). \[\dot{P}=C_{DT}\cdot 0.5\cdot\rho\cdot A\cdot v_{c}^{3} \tag{6}\]  
where the density of the air is 1.225 kg/m\({}^{3}\). To generalise the result, the normalised power losses are shown in Table 6.  
In the most extreme condition, the loss was 6.7 times larger than that in the symmetrical case.