# Experimental Investigation in Drag Coefficient of Cubes
## 5 Conclusions  
This study performed free settling experiments with uniform and spliced cubes to characterize the relationship between drag coefficients and both Reynolds number and orientation angles, revealing several important findings on the effects of orientation angle on drag coefficients.  
The drag coefficient of the cube is always higher than that of the sphere in the same Reynolds number, especially at the range of \(Re>258\). When the Reynolds number is larger than 100, the discrete degree of the drag coefficient obtained by the uniformed cube free settling becomes larger and more complex. This is because the orientation angle of the cube varies significantly during the free settling process when the Reynolds number is larger than 100.  
The non-uniformed spliced cube can maintain a stable orientation angle in experiment conditions under the effect of the eccentric moment. In particular, the orientation angle of the spliced cube with \(h/a=0.5\) and \(h/a=1.0\) can be maintained at \(0^{\circ}\) and \(45^{\circ}\) in a range of \(4.5\times 10^{-1}\leq Re\leq 4.516\times 10^{3}\), respectively. According to the experimental data, the orientation angle has different effects on the drag coefficient of the cube in different Reynolds number ranges. When the Reynolds number is in the range of \(Re<10\) and \(Re>1\times 10^{3}\), the orientation angle has little effect on the drag coefficient of the cube. While the Reynolds number is in the range of \(10<Re<1\times 10^{3}\), the drag coefficient of the cube is in direct proportion to its orientation angle. The upper and lower bound of the cube drag coefficient in this Reynolds number range is that obtained by the cube with the orientation angle of \(45^{\circ}\) and that with the orientation angle of \(0^{\circ}\), respectively. Based on the  
Figure 10: Compression between the predicted drag coefficients by Equation (8) and cube drag coefficients in the previous works [10; 11; 12; 14; 17; 23; 25; 26].  
characteristic behaviors of the drag coefficient observed in this study, we propose a new simple yet accurate piecewise correlation model for cube drag coefficients. The correlation model is a piecewise function with a similar form in three Reynolds number ranges, which are 0.4 < \(Re\) < 10, 10 < \(Re\) < 1 \(\times\) 10\({}^{3}\) and 1 \(\times\) 10\({}^{3}\) < \(Re\) < 4.516 \(\times\) 10\({}^{3}\). The drag correlation model shows a good agreement with the experimental data as well as the data reported in previous studies.  
Conceptualization, Y.Z.; investigation, J.W., H.M., J.N., D.C. and M.C.; methodology, Y.Z. and H.M.; formal analysis, J.W., H.M. and J.N.; project administration, Y.Z.; supervision, Y.Z. and D.C.; Validation, J.N. and M.C.; writing--original draft, J.W.; writing--review and editing, D.C. and M.C. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Science and Technology Major Project J2019-II-0014-0035 and Defense Industrial Technology Development Program GJCZ-010-2024-0005.  
Not applicable.  
The data within the article can be made available upon request.  
Authors [PERSON] and [PERSON] were employed by the company AECC Sichuan Gas Turbine Establishment and Author [PERSON] was employed by the company Aero Engine Corporation of China. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.