# Experimental and Numerical Investigation on Ballast Flight from Perspective of Individual Particles
## 2 Materials and Methods
### Wind Tunnel Experiment  
The wind tunnel experiment of ballast particles was carried out to investigate the occurrence and development of ballast flight from the perspective of individual particles. The ballast dynamics characteristics under wind load, as well as the influence of mass, shape, and windward direction on ballast flight were analyzed. As shown in Figure 3, a board (2.5 m \(\times\) 2 m) was fixed as the test bench in the wind tunnel laboratory. It was 0.35 m between the test bench and ground, which was the same as the thickness of the ballast bed. A transparent plexiglass plate was fixed above the test bench to simulate the bottom of a train carriage, through which the movement of the ballast could be observed clearly. The wind speed from the inlet of the wind tunnel laboratory could be adjusted by controlling the fan voltage. A Pitot tube was set up to monitor the wind speed above the test bench. The test bench, plexiglass board, and Pitot tube were fixed firmly in case of vibration under the strong wind. In addition, the multi-layer protective nets were installed at the end of the test bench as well as the outlet of the wind tunnel laboratory, which could prevent the ballast from flying out of the bench and causing damage to the fan. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **A15** & **B15** & **C15** & **D15** \\ \hline
**Long axis** & 5.53 cm & 7.34 cm & 9.18 cm & 10.39 cm \\
**Middle axis** & 5.45 cm & 4.46 cm & 8.69 cm & 5.16 cm \\
**Short axis** & 3.86 cm & 3.97 cm & 1.86 cm & 2.61 cm \\
**Mass** & 149 g & 151 g & 148 g & 150 g \\
**Volume** & 54.18 cm\({}^{3}\) & 55.66 cm\({}^{3}\) & 52.86 cm\({}^{3}\) & 53.96 cm\({}^{3}\) \\
**Surface area** & 80.39 cm\({}^{2}\) & 89.86 cm\({}^{2}\) & 120.52 cm\({}^{2}\) & 102.94 cm\({}^{2}\) \\
**Acicular index** & 1.02 & 1.65 & 1.06 & 2.01 \\
**Flakiness index** & 0.71 & 0.89 & 0.21 & 0.51 \\
**Actual ballast** & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Database of ballast information. Figure 2: Ballast samples. The ballast samples in the four groups were tested respectively, and there were eight ballast particles to be tested in each case because of the tremendous number of samples. The light particles were easy to be blown off if light and heavy ballast particles were tested simultaneously. So, the light samples (A1, A2, B1, B2, C1, C2, D1, and D2) were arranged in a single test. The remaining ballast samples were tested in the order of A3-A10, A11-A18, B3-B10, B11-B18, C3-C10, C11-C18, D3-D10 and D11-D18. The ballast samples were arranged at the front of the test bench in accordance with their sequence in each group, as shown in Figure 4.  
The shapes and sizes of the surface were similar in different placement directions between the spherical ballast (Group A) and oblate ballast (Group C), while these properties of ellipsoid ballast (Group B) and prolate ballast (Group D) were affected by the placement direction greatly. For this reason, the ballast samples of Groups B and D were set as the long side faces the wind and short side faces the wind, respectively, as shown in Figure 5, to investigate the influence of the windward direction of the ballast on its dynamics and critical velocity. Figure 4: The wind tunnel experiment of ballast particles with different shapes and mass. Figure 3: The schematic diagram of the experiment equipment. The mean velocity above the ballast bed is close to 1/3 of the train speed [12]. Therefore, the input velocity \(\
u\) in the experiment could represent the airflow generated by the train with a speed of 3\(\
u\). The wind speed was increased step by step during the test. The movement of each ballast sample under wind load was recorded by the high-speed camera in the wind tunnel laboratory, and the wind speed was obtained correspondingly. It was difficult to prevent the ballast flying once it had the initial displacement under wind load. Therefore, it was necessary to control the initial displacement of the ballast to prevent ballast flight.