# Quantitative Analysis of Drag Reduction Methods for Blunt Shaped Automobiles
## 2 Literature Review
### Aerodynamic Drag  
When an object is placed in a flow, or when an object is moving in fluid, forces are applied to its surface. Former cases are referred to analytical measurements while latter is a real-life approach. These two cases could be compared and gives us similar results with adequate restrictions. These forces, due to shear stress, try to decrease speed of movement; thus, energy is dissipated. This kinetic energy loss is converted to heat energy. The dissipation rate is amplified at high velocities above subsonic level. In those cases, examined fluid regions cannot be considered incompressible and isothermal. Due to regional speed limit regulations, ground vehicles are far from the speed of sound. For that reason, it is possible to consider the air isothermal and incompressible. In Figure 1, an object is immersed in air flow and the affected forces can be seen. In front of the body (indicated with red) pressure drag is created, which is one of the crucial aerodynamic losses that can occur on a body. On the sides (indicated with green), skin friction losses could only cause minor drag. Magnitude can be amplified if complex geometry creates flow separation. Similarly, to the frontal, side force is applied on the body to the direction of the flow on the rear (indicated with blue). The flow also creates drag and lower pressure to the ambient pressure. Thus, it can be called negative pressure zone, or wake region, in attribute to its highly turbulent behaviour, where vortex shedding and recirculation bubbles could appear. In [PERSON] et al. [7], it was concluded that the rear end flow has more impact on the drag than on the frontal side. The drag force coefficient (C\({}_{\text{D}}\)) is the function of the drag force (F\({}_{\text{D}}\)) acted on the vehicle surface; \(\rho\) and \(\
u\) are the density and the flow velocity, respectively. A is the projection area of the vehicle, in the direction of the movement. \[\text{C}_{\text{D}}=\text{F}_{\text{D}}\cdot(0.5\cdot\
u^{2}\cdot\text{A})^{-1} \tag{1}\]  
C\({}_{\text{D}}\) considered to be a quasi-constant value. However, [PERSON] [8] shows that at lower velocities (15 m s\({}^{-1}\)), it does not have linear connection with F\({}_{\text{D}}\). Furthermore, C\({}_{\text{D}}\) should be a time averaged value, due to vortex shedding. Drag force can be experimentally determined in wind tunnels where the body is attached to a force sensor. If full-scale measurement cannot be performed in wind tunnels, small-scale measurements can be made. A smaller scale with the combination of a low-Reynolds (Re) number could make the force sensor inadequate for F\({}_{\text{D}}\) measurements. [PERSON] et al. [9] concluded that the Re = \(3\times 10^{5}\) leads to a 2% overall difference in the drag coefficient. [PERSON] [8] reported 1.7% uncertainty in his work. C\({}_{\text{D}}\) measurement accuracy can be increased to 0.05% [10]. The drag reduction is often measured in Count, which is equal to 0.001 C\({}_{\text{D}}\) change compared to the initial. For example, if a vehicle with C\({}_{\text{D}}\) = 0.3 measured with a method that has 0.05% inaccuracy, the drag reduction below 0.15 Counts just as a measurement error. [PERSON] [11] has published a more detailed method to calculate wind average drag coefficient for on-road measurements where the road inclination, wind speed magnitude, and direction were included. However, in the examined studies, C\({}_{\text{D}}\) is simplified since vehicles are examined in wind tunnels and numerical models. [PERSON] et al. [12] made on-road measurements with logged external parameters where vehicle speed fuel consumption and drag estimation were also measured; these are precise values. However, for design period, it is not possible, which is why it is essential to know what method leads to greater drag reduction. For this paper, an important parameter is the drag reduction (DR), which is the percentile reduction of the initial.