# Aerodynamic Drag Reduction on Speed Skating Helmet by Surface Structures
## 3 Experiment Method and Fabrication Process  
A full-scale skater model without arms or legs was used in the wind tunnel experiment. This model was obtained by scanning an athlete in skating posture with the head tilted to 45\({}^{\circ}\). In order to simulate the actual competition process as much as possible, the head, the face, and the neck, which were close to the helmet in the model, were completely preserved, while the lower part of the torso was simplified to reduce the resistance. Moreover, the cross-section of the simplified lower support was streamlined, as shown in Figure 1. The point of this treatment was that the change in resistance with speed would be more stable compared with a cylindrical support, which helped to reduce experimental errors. There were some marks on the head of this model to ensure that the test helmets would be at the same position every time, in order to reduce the systematic errors. The schematic of the wind tunnel experiment is shown in Figure 6. \begin{table}
\begin{tabular}{c c c} \hline
**Mesh** & **Elements** & \(C_{d}\) \\ \hline M1 & 7,316,086 & 0.32416 \\ M2 & 8,779,304 & 0.33005 \\ M3 & 14,505,131 & 0.33202 \\ M4 & 20,200,985 & 0.3322 \\ \hline \end{tabular}
\end{table} 
Table 1: The finite element mesh used in simulations and the results of the grid convergence study. Figure 5: Grid convergence study for \(C_{d}\) with respect to the number of elements in the computational domain. The experiments were conducted in an open jet wind tunnel which had a rectangular cross section of 2.5 m \(\times\) 3 m (width \(\times\) height). This wind tunnel was specially designed for sports training and has high flow field quality. The turbulence intensity was less than 0.75%; therefore, the velocity is consistent, with very little fluctuation. The boundary layer thickness near the wind tunnel ground was measured at a velocity of 20 m/s, and the result showed that the thickness was about 80 mm, which was much smaller than the height of the mannequin. The blockage ratio was approximately 3% in our experiments. The whole test object was placed in the center of the wind tunnel and about 4 m from the outlet. The experiments were performed in a series free stream velocities (\(U\)) from 6 m/s to 24 m/s. The Reynolds number (\(Re=WU/\
u\), where \(U\), \(W\), and \(\
u\) were the free stream velocity, the helmet width, and the kinematic viscosity of the air, respectively) based on the free stream velocity and the helmet width was from \(1\times 10^{4}\) to \(2\times 10^{5}\). The drag force on the model was measured by a force balance installed under the test platform of the wind tunnel. The measuring range of the balance was 300 N in the streamwise direction. The balance was also calibrated before the experiment, and the uncertainty was less than 0.07%. The sampling frequency in this experiment was 1200 Hz, and the sampling time on each velocity value was 10 s. Each helmet was measured for five rounds to reduce the systematic error, and the results were averaged, with standard deviations calculated. Four types of helmets were tested in this wind tunnel experiment, including three helmets with surface structures and one original helmet without any structure as the control. Figure 7a shows the distribution of surface structures on tested helmets. The helmet surface was divided into three parts, where different types of surface structures were used. Region A and C were located on the sides of the helmet, while region B was on the top. According to the helmet shape and the drag reduction effect of the surface structure, the riblet structure had been used in Region A and C on all structured helmets. The surface structure used in region B had two types, namely riblets and bumps. as shown in Figure 7b,c.