# Experimental and Numerical Investigation on Ballast Flight from Perspective of Individual Particles
## 3 Results and Discussions
### Simulation Results  
#### 3.2.1 Pressure Difference of Ballast Particle  
There is a pressure difference between different ballast surfaces under different wind conditions. When the pressure is larger than that keeping the ballast stable, the particle would fly. The parameter \(P\) is introduced to analyze the flow characteristics of ballast particles, which could represent the pressure difference as follows:  
\[P=P_{p}-P_{n} \tag{7}\]  
where \(P_{p}\) and \(P_{n}\) refer to the maximum air pressure of positive and negative acting on the ballast surface respectively. All numerical models of ballast samples were simulated according to the grouping scheme in the wind tunnel experiment. Then, the air pressure difference \(P\) was calculated based on Equation (7). Figure 14 shows the pressure difference of ballast particles with four shapes and two windward directions at a wind speed of 30 m/s. B_1 and D_1 represent the long sides of particle B and D facing the wind, while B_2 and D_2 represent the short sides facing the wind. The mass and volume of ballast samples increase with their number sequence in Figure 14. Since the flow characteristic is independent of the mass in CFD simulation, the pressure difference among the ballast particles in each group increases with their volume. The reason is that the windward surface of the ballast particles increases with their enlarged volume, and the maximum positive and negative pressure increase at the same time under the condition of the constant wind speed and ballast shape. Thus, the pressure difference among the ballast surfaces increases accordingly. Compared with Figure 11, the pressure difference in Figure 14 gets higher with the increase of ballast volume, which indicates that the ballast particle is easy to fly. In Figure 11, the critical velocity gets higher with the increase of ballast mass, which is unlikely to trigger ballast flight. However, the ballast volume increases with its mass on the basis of the same shape, so the rule in Figure 14 is in contradiction with that in Figure 11. The result shows that although the pressure difference increases with the ballast volume, the ballast mass would increase with it as well. The ballast flight will occur only when the pressure is large enough to overcome the larger load derived from its increased mass. That is, although the ballast volume increases with its mass, the influence of mass on ballast flight is more significant  
Figure 14: Air pressure difference of ballast particles at a wind speed of 30 m/s. than that of the volume. Therefore, the ballast with a higher density on the top of ballast bed is more effective than the ballast with a larger size to prevent ballast flight. Besides, the shape of the ballast also has an influence on the pressure difference, and the influence is consistent with the conclusion in the wind tunnel experiment. As shown in Figure 14, under the condition of the same volume, the pressure difference of the ellipsoid ballast is the largest, and it is the easiest to fly, followed by the sphere ballast and prolate ballast. The pressure difference of the oblate ballast is the smallest, and it is the least likely to fly. When the ballast volume (number) is the minimum, the pressure difference of the six ballast models is similar, which is from 701 Pa (C1) to 757 Pa (B1_1). With the increasing of the volume (number), there is a significant difference in the increasing range of the pressure difference between various groups. When the volume increases to the maximum, the increase of the pressure difference of sample B with the long side facing the wind is the largest (90.6%), followed by that of sample B with the short side facing the wind (86.8%), and sample C is the smallest (49.6%). The results show that the volume increase of the ellipsoid ballast has the most significant effect on ballast flight, especially when the long side faces the wind. In addition, in order to prevent ballast flight, the height of ballast bed level could be reduced, and the space between sleepers could be optimized.