# Aerodynamic Drag Reduction on Speed Skating Helmet by Surface Structures
## 4 Results and Discussion  
### CFD and Experiment Results  
The free stream velocity of the CFD simulations was 14 m/s (\(Re=2.3\times 10^{5}\)) in this research, because it was the typical velocity in competitions. The drag coefficients of the CFD results were summarized in Figure 10. It was found that the drag coefficient of the bumped helmet model was lower than others, which was consistent with the wind tunnel experiment results. The rate of drag reduction (\(\eta\)) can be defined as  
\[\eta=\frac{F_{d1}-F_{d2}}{F_{d1}}\times 100\% \tag{6}\]  
where \(F_{d1}\) and \(F_{d2}\) are the drag forces of the helmets with and without surface structure, respectively. The drag reduction rate of the riblet helmet and the bump helmet compared with original helmet model were approximately 2.4% and 4.2%, respectively. According to the CFD results, the drags of structured helmets were measured by experiment. In addition, a helmet with smaller space between bumps (type 4) was tested to further analyze the drag reduction effect of the bump structure. The experiment results are plotted in Figure 11, where the \(C_{d}\) values are averaged over five rounds of the sampling process. The error bars based on the standard deviation are also presented in Figure 10a, and the relative standard deviation was less than 1.4%. As shown in Figure 11a, \(C_{d}\) of all tested helmets kept a high value when \(Re\) was less than \(1.2\times 10^{5}\), and showed a significant decrease as \(Re\) increased from \(1\times 10^{5}\) to \(2\times 10^{5}\). This phenomenon was due to the torso and supporter of the model, and the helmets had a less significant impact on that. It was clear that the \(C_{d}\) of the original helmet was higher than that of structured helmets. Figure 11b shows the \(\eta\) of structured helmets compared with those without surface structure. It was found that the range of \(Re\) based on free stream velocity could be divided into two parts, as \(Re<1.4\times 10^{5}\) and \(Re>1.4\times 10^{5}\), according to the \(\eta\) of the structured helmets. For the range of \(Re<1.4\times 10^{5}\), the drag of the type 2 helmet was lower than the drag of others, and the \(\eta\) value of the type 2 helmet was approximately 9% in \(Re=\)1.2\(\times\) 10\({}^{5}\). However, when \(Re>1.4\times 10^{5}\), the \(\eta\) of the type 3 helmet was significantly higher than the others (approximately 7% in \(Re=2\times 10^{5}\)). During competitions, the usual velocities of athletes are approximately 10-20 m/s, corresponding to a \(Re\) range of \(1.6\times 10^{5}\) and \(3.2\times 10^{5}\). As a result, the type 3 helmet with the bump will have lower drag than others in this velocity range. Figure 10: Drag coefficient of the results for three types of helmets used in the CFD simulations. For all structured helmets, the \(\eta\) values varied similarly in the range of \(Re>1.4\times 10^{5}\), which indicated that the surface structures of the helmets caused the increased aerodynamic resistance with the increasing free stream velocity. For the type 1 riblet helmet, the downward trend of \(\eta\) was more significant than others, and when \(Re>3\times 10^{5}\), the drag for the type 1 helmet was higher than original helmet as the \(\eta\) went to negative value. For type 2 and type 3 helmets, which both had bumps at the middle region, the trend of \(\eta\) decreased in a similar way, especially in \(Re>3\times 10^{5}\). From the results of the CFD analysis and wind tunnel experiments, it was clear that both riblet and bump structures had obvious drag reduction effects on the skating helmet. According to the CFD results, the drag for the bumped helmet was lower than that of the riblet one, which was verified by the experiment results. The bumped helmet with small spacing (type 4) was the best model with the lowest drag in the wind tunnel experiments.