# The Refined Simulation Methods of Fluctuating Wind and Aerodynamic Forces Relative to Moving Trains
## 5 The Aerodynamic Force Simulation of Moving Trains
### The Comparison of Unsteady Aerodynamic Forces  
This section assumes the train moves in the homogeneous and stationary wind environment with the same train and wind speeds adopted above. In order to validate the derived aerodynamics model of moving trains, only considering the along-wind fluctuating wind, three types of lateral aerodynamic forces for the moving train are generated and compared with the tested aerodynamic coefficients [7]: 1 the quasi-steady aerodynamic force, simulated by Equation (23), ignores the effects of the admittance function; 2 the unsteady aerodynamic force, generated by Equation (33), takes the amplitude and phase of the admittance function into consideration; and 3 the unsteady aerodynamic force, simulated by Equation (48), only considers the amplitude of the admittance function, i.e., the existing simulation methodology proposed by [PERSON]. The results are shown in Figure 7.  
It can be seen that the time histories of unsteady aerodynamic forces are smoother than those of quasi-steady aerodynamic forces. The admittance function filters out the high-frequency components of the aerodynamic force, decreasing the peak value of the unsteady aerodynamic force. The aerodynamic force generated by the proposed rational function fitting method in this paper generally agrees with that of the weighted function  
Figure 6: The target value and the fitting value of the lateral force admittance function.  
Figure 7: The lateral forces for moving trains induced by the fluctuating wind: (**a**) the time history of lateral force in 0 to 120 s; (**b**) the enlarged time history of lateral force in 84 to 96 s.  
method proposed by [PERSON], which verifies the correctness of the rational function fitting method. Enlarging time history in the range of 84-96 s, a time lag is observed in the aerodynamic force when the phase of the admittance function is considered, indicating that the rational function fitting method could effectively present the phase characteristic of the admittance function in the time domain. Since the phase angle calculated by Equation (46) is relatively small, the aerodynamic 'delay' considering the admittance function phase is also small. At present, the research on the complex admittance function of a train is still rare, lacking the test results of the complex admittance function of the train. However, further investigation remains necessary to determine the phase difference characteristics of the unsteady aerodynamic forces for the moving trains.  
The train overturning is directly relevant to the rolling moment around the leeward rail, which is the resultant moment of the side force, lift force, and the torsional moment around the axis of the vehicle body. The torsional moment of the vehicle body is generally small enough to be neglected [8]. The phase difference between the side and lift forces is characterized by the phase of admittance functions, which means that side and lift forces cannot reach the maximum simultaneously. In practical applications, simulating the aerodynamic forces of moving trains with the proposed methods can improve train safety assessment in regions with complex wind environments.