# Experimental and Numerical Investigation on Ballast Flight from Perspective of Individual Particles
## 3 Results and Discussions
### Experimental Results
#### 3.1.2 Influence of Ballast Properties  
The critical velocity could judge the difficulty of ballast flight, and the data of ballast particles with different mass and shapes are shown in Figure 11. It can be seen that the critical velocity increases with the ballast mass in general. The ellipsoid ballast B1 (5 g) is the first to move at the wind speed of 14.22 m/s, and it is the easiest to fly under wind load. When the wind speed is 29.89 m/s, all the particles are blown off. The oblate ballast C18 (200 g) moves at last, and it is the least likely to fly under wind load. The critical velocity of ballast particles with similar quality but different shapes is quite different. The ellipsoid ballast (Group B) has the minimum critical velocity, and it is the easiest to fly. The spherical ballast (Group A) and the prolate ballast (Group D) are the second sequentially. The oblate ballast (Group C) has the maximum critical velocity, and it is the least likely to fly. In other words, the critical velocity turns higher as the ballast particles become smaller and more flat. When the mass of ballast particles in different shapes increases from 5 g to 200 g, the largest increase of the critical velocity is the oblate ballast, reaching 84.2%. It is concluded that the influence of the mass change of the oblate ballast on its critical velocity is more significant than that of the other shapes, so the oblate ballast is unlikely to fly with the same mass increasing.  
Figure 11: Critical velocity of ballast particles with different mass and shapes.  
Figure 10: The ballast movement in a wind tunnel experiment.  
However, the critical velocities shown in Figure 11 also have some abnormal fluctuations, such as those of ballast A8, B5, C7, and D14. Although the mass of ballast B5 is larger than that of B4, B5 is more likely to fly under wind load. The abnormal fluctuation is not derived from the accidental error, because the data is the result of repeat tests under the same condition. Figure 12 shows the stability analysis of ballast B5. B5 will be in the most stable situation when it stands on the plane on which its long axis and middle axis are located. The plane is defined as \"the stable placed surface\", which is shown by the red area in Figure 12b. B5 was placed with the bottom of its stable placed surface in the wind tunnel test. However, there are two raised edges on the stable placed surface of B5, as shown in Figure 12c. The contact between the ballast and test bench is a point-to-surface contact with three points (P1, P2, and P3) on the raised edges of the stable placed surface. Therefore, the ballast similar to B5 is easy to vibrate under wind load. As the wind speed increases gradually, the ballast particle is more likely to fly. For this reason, although the mass of B5 is larger than that of B4, its critical velocity is still lower, which results in the irregular fluctuation of the critical velocity in Figure 11. The irregular fluctuations of other ballast particles are similar, and they are not described here.  
In order to investigate the influence of the windward direction of the particles on ballast flight, the ellipsoid ballast (Group B) and prolate ballast (Group D) with different windward surfaces were tested respectively. The critical velocities of the ballast particles with different windward surfaces are shown in Figure 13. It can be seen that the particles with large acicular indexes have different critical velocities when they are in different windward directions. When the windward surface of the ballast is adjusted from the long side to the short side, the critical velocity of the ellipsoid ballast and prolate ballast increase by 0.45-0.59 m/s and 0.32-0.44 m/s, respectively.  
Figure 12: Stability analysis of ballast B5. (**a**) Actual ballast; (**b**) The stable placed surface; (**c**) The raised edges and points.  
Figure 13: Critical velocity of ballast particles with different windward surfaces.