# Research on the Aerodynamic Characteristics of Tractor-Trailers with a Parametric Cab Design
## 3 Results and Discussion  
The \(\mathbf{C_{d}}\) is regarded as a major indicator that represents the aerodynamic performance of a vehicle; Table 4 illustrates the results of the CFD simulations of parametric designed tractor-trailer models with different cab variants. The impact of different geometrical modifications on the drag characteristics is shown in Table 4. In this table, \(\Delta\mathbf{C_{d}}\) represents the change rate of the \(\mathbf{C_{d}}\) its calculated equation is \(\Delta\mathbf{C_{d}}\) = \(\mathbf{C_{d}}-\mathbf{C_{d-baseline}}\)/\(\mathbf{C_{d-baseline}}\), the symbol '\(-\)' in the table represents the decreased of \(\mathbf{C_{d}}\); conversely, the symbol '+' represents the increased of \(\mathbf{C_{d}}\). It can be seen that in all cases, the \(\mathbf{C_{d}}\) decreased, except for the 400 mm-135 degrees case, and the maximum drag reduction rate compared with the baseline model was about 8.49%. These results imply that the protruding part of the cab and changing its dimensions have a distinct influence on the aerodynamic characteristics of tractor-trailers. It is interesting to note that when the angle between the protruding part and A pillar was fixed, the length of this part increased from 400 mm to 600 mm; the \(\mathbf{C_{d}}\) first decreased and then increased. When the length was fixed in the 500 mm cases, the aerodynamic drag reduction was most pronounced. When the included angle was 120 degrees and the length of the protruding part was 400 mm, the minimum \(\mathbf{C_{d}}\) was 0.4298. When the included angles were 125 degrees, 130 degrees, and 135 degrees, the different parametric cab design vehicles with the \(\mathbf{C_{d}}\) were 0.4234, 0.4281, and 0.4260, respectively, and the prominent length was 500 mm; the \(\mathbf{C_{d}}\) was the smallest. It showed that when the extended length was 500 mm, the rate of aerodynamic drag reduction was generally higher, and this dimension was a more suitable drag reduction length for the reference tractor-trailer model. However, when the protruding length was fixed, the change in \(\mathbf{C_{d}}\) was more complicated. When the extended length was 400 mm and 600 mm, the aerodynamic \(\mathbf{C_{d}}\) first increased and then decreased with the increased of the angle. When the length was 500 mm, the change of angle had little effect on aerodynamic drag. The aerodynamic drag force on a vehicle is dependent on the form, and is caused by the pressure difference induced by massive flow separation. The present resolution was thought to be reasonable to investigate flow phenomena over the tractor-trailer and to explain the drag reduction mechanism. The 500 mm-125 degrees case had the most pronounced drag reduction effect; therefore, the numerical simulation results of this model were compared with the baseline model, and the related drag reduction mechanism was analyzed in Section 3.2. Meanwhile, due to the influence of the included angle and \begin{table}
\begin{tabular}{c c c} \hline \hline
**Cab Model** & \(\mathbf{C_{d}}\) & \(\mathbf{\Delta\mathbf{C_{d}}}\) \\ \hline
**400 mm-120 degrees** & 0.4298 & \(-\)7.11\% \\
**400 mm-125 degrees** & 0.4351 & \(-\)5.96\% \\
**400 mm-130 degrees** & 0.4341 & \(-\)6.18\% \\
**400 mm-135 degrees** & 0.4982 & \(+\)7.67\% \\
**500 mm-120 degrees** & 0.4402 & \(-\)4.86\% \\
**500 mm-125 degrees** & 0.4234 & \(-\)8.49\% \\
**500 mm-130 degrees** & 0.4281 & \(-\)7.47\% \\
**500 mm-135 degrees** & 0.4260 & \(-\)7.93\% \\
**600 mm-120 degrees** & 0.4459 & \(-\)3.63\% \\
**600 mm-125 degrees** & 0.4501 & \(-\)2.72\% \\
**600 mm-130 degrees** & 0.4280 & \(-\)7.50\% \\
**600 mm-135 degrees** & 0.4442 & \(-\)4.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Aerodynamic drag coefficient of new cab design models. \begin{table}
\begin{tabular}{c c} \hline \hline
**Experiment V = 25 m/s** & \(\mathbf{C_{d-baseline}}\) \\ \hline Wind tunnel & 0.4507 \\ Numerical simulation & 0.4613 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Drag coefficient of the tractor-trailer baseline model.