# Quantitative Analysis of Drag Reduction Methods for Blunt Shaped Automobiles
## 3 Quantitative Analysis  
A quantitative study was made for the evaluation of the referenced methods. During the literature search, 417 papers were screened, and 100 papers were mentioned in the study for analysis. Moreover, 32 research papers had relevant validated results between the beginning of 2008 and April 2020. The low number can be attributed to the over-specified research area. Most drag related problems discussed VG at supersonic velocity regime or for thermal related tasks. For drag reduction analysis, the active shape and topology categories are divided into subcategories, such as SJA and SJF for active, Fairing (and side skirts) for shape, and topology drag reduction methods for Flap and Winglet. There was a sixth subcategory; those that were not in the first five subcategories due to their uniqueness were categorized as \"other\" subcategory. For the analysis, initial drag coefficient (C\({}_{\text{Dinitial}}\)), drag reduction (DR), and Count were used. Initial drag coefficients were presented in a boxplot (see Figure 5), where values ranged from 0.08 [19] to 0.98 [47], and the median value was 0.35. Minimum and maximum values were peaking values, most of them clustered to the C\({}_{\text{Dinitial}}\) mean value, which was 0.44 with \(\pm\)0.21 standard deviation. Figure 5: Initial drag coefficient boxplot; (line is median, \(\square\) mean, \(\blacklozenge\) peaking values, synthetic jet actuators (SJA), steady jet flow (SJF).). For SJF, only three methods were used, that is why was the quartile range was so large. SJA Fairings, Winglets, and other subcategories had peaking values. Similar magnitudes were not found during the literature research. The purpose of Figure 5 is to visualize the initial C\({}_{\text{D}}\) of the vehicle to help further evaluations. DR and Count comparison were made separately since the linear regression (R\({}^{2}\)) of the value connection was weak (R\({}^{2}\) = 0.26). This connection can be seen on Figure 6. Percentile change (DR) evaluation can be more effective with high C\({}_{\text{Dinitial}}\) bluff vehicles, while aerodynamic vehicle Count could show some slight differences. Values that were above the regression line were above the mean C\({}_{\text{Dinitial}}\) value. For better comparison, both DR and Count values are presented in Figure 7,b. Quartile ranges were different due to C\({}_{\text{Dinitial}}\) (Count = 10-DR C\({}_{\text{Dinitial}}\)). Overall, in all 32 researches and 43 included cases, mean DR was 13.67% \(\pm\) 14.06%. Negative DR (C\({}_{\text{D}}\) increase was not observed), the lowest was 1.17% and maximum was 90%. Median from these were 10%. Out of the 43, 21 cases had higher value than the mean value. From these, there were 7 active, 5 shape, and 9 topology cases (see Tables 1-3). Highest DR = 90% was achieved by [PERSON] et al. (2010) in 2012. Later, this was reproduced with a numerical simulation by [PERSON] et al. (1994), which showed lower (DR = 9.04%). It has to be  
Figure 6: Connection between Count and Drag reduction (line fitted curve with R\({}^{2}\) = 0.26). Figure 7: Reduced drag boxplot in (**a**) percentage and (**b**) in Count (line is median, \(\square\) mean, \(\blacklozenge\) peaking values). noted that the experimental measurement was done at 2.5 m s\({}^{-1}\), which could lead to over prediction. [PERSON] et al. [100] also showed that this DR could be reduced to 20% at higher velocities. Count mean value was 55.58 \(\pm\) 45; the DR = 90% was not notable since the corresponding C\({}_{\text{Dinitial}}\) was low [100]. When Count is ranked, only 15 cases had higher than 56 with 6 shapes (3 in the top 3), 5 topology, and 4 cases with active methods. For DR SJF (18.33%) and SJA (12.75%), active methods are favourable, since these had the highest median values from the subcategories (see Figure 7a). As for Count, Fairings (97), and SJF (79) were favourable (see Figure 7b). The Flap and Winglet subcategories had the lowest mean and median DR and Count values. The two most favourable categories were the SJF and Fairings.