## 4 Results and Discussion
### Aerodynamic Noise Characteristics
#### 4.2.3 Aerodynamic Noise Directivity  
In this section, the aerodynamic noise directivity around the pantograph with the different configurations is presented. According to the ISO3095-2013 standard [33], the far-field noise receivers should be located 7.5 or 25 m away from the center line of the track and 1.2 or 3.5 m above the ground. The present study investigates the far-field noise characteristics around the pantograph with a distance of 7.5 m in the radial direction and 3.5 m above the ground. The OASPL in the X-Y, Y-Z and X-Z planes is discussed, as shown in Figure 19, and the OASPL is considered at every five degrees. It is found that in all the planes the noise directivity induced by the sunken pantograph is slightly smaller than the flush pantograph in general. Only at some angles, the noise induced by the sunken pantograph is equal to or larger than that by the flush pantograph. Besides, some interesting phenomena are observed in each plane. First, in the X-Y plane, when the pantograph is used with the flush surface, a relatively high OASPL is found in the rear arc of the pantograph (\(-5^{\circ}\leq\theta\leq 5^{\circ}\)), and along the sideline over the ranges \(85^{\circ}\leq\theta\leq 125^{\circ}\) and \(235^{\circ}\leq\theta\leq 275^{\circ}\). When the pantograph is installed in the sunken surface, the rear arc still has the higher OASPL. However, the high OASPL values are also predicted at other angles. In the down-pantograph, a large part of the structure is located inside the cavity. The corresponding amplitude of the four corners of the cavity is slightly higher than that of other positions. This may be because of the effects of the sunken configuration. Specifically, during the process of noise propagation, the sound wave can reflect within the cavity of the sunken surface, four corners can easily become the convergence area of reflected sound waves. One can see that the directivity of noise is not completely symmetrical the X-Y plane. Similar instances of incomplete symmetry are also reported in the literature [13]. The main reason is that the far-field noise monitors are usually placed at  
Figure 18: Comparison of OASPL at different distances of pantographs with different configuration bases: (**a**) with pantograph as reference position, OASPL at different vertical distances from center line of track in horizontal plane; and (**b**) OASPL of up- and down-pantograph with different configuration bases at different monitoring points along moving direction of train. every 5-10 degrees around the pantograph in different planes. This may omit part of the amplitude between the monitors, resulting a certain impact on the results. In addition, in the calculation of the sound field, the frequency resolution has a slight impact on the results. However, further detailed analysis of the up- and down-pantograph in the cavity has shown that there is almost no difference when the frequency resolution is increased from 10 Hz to 5 Hz, namely, the overall noise difference is less than 1 dB. In the Y-Z plane, the noise distributions obtained by the two installation bases are nearly symmetric and the higher sound level area is found in in the range of \(60^{\circ}\leq 9\leq 120^{\circ}\). It also shows that, in this range of theta with the pantograph under the down configuration, the OASPL obtained by the flush installation base is higher than that by the sunken base configuration. However, under the up-pantograph condition, the OASPL values obtained by the two configuration bases are close to each other. In the X-Z plane, the down-pantograph with the flush base produces higher noise than the sunken base in all directions. For the up-pantograph, the noise amplitudes of the flush and sunken bases are very close to each other in general. Nonetheless, it is seen that at some angles, the noise induced by the sunken base is higher than the flush base.