# Wind Characteristics in Mountainous Valleys Obtained through Field Measurement
## 3 Results
### Mean Characteristics
#### 3.1.3 Wind Attack Angle at Mean Wind Speed  
The wind attack angle of the mean wind speed is the angle between the main direction of the incoming wind flow and horizontal. The following formula was used for the calculation:  
\[\alpha=\arcsin(\frac{u_{z}}{\sqrt{u_{x}^{2}+u_{y}^{2}}}) \tag{2}\]  
where \(u_{x}\) is the wind speed in the \(x\)-direction, \(u_{y}\) is the wind speed in the \(y\)-direction, \(u_{z}\) is the wind speed in the \(z\)-direction, and \(\alpha\in(-90^{\circ},90^{\circ})\).  
In the study of wind-induced vibration, the wind attack angle significantly affects the aerodynamic stability of a bridge, so it is important to accurately determine the distribution of the wind attack angle. Usually, the recommended value for wind resistance studies of bridges is \(-3^{\circ}\) to \(+3^{\circ}\), but this range is only applicable to flat and open areas. Therefore, different from the recommendations of the specifications, the wind resistance study of mountain bridges needs to consider the situation of large angles of attack. When conducting wind tunnel tests, it is even necessary to adjust the wind attack angle to \(10^{\circ}\), as Figure 12 shows that the wind attack angles corresponding to each height are discrete in the height range of 30-200 m. Meanwhile, the discrete range of wind attack angles gradually decreases with the increase in height above the ground. At low altitudes below 60 m above the ground, the absolute value of the wind attack angle is large and can even reach nearly \(20^{\circ}\). The reason for this finding is that the low altitude is strongly influenced by the terrain, and the wind speed is low, so the air turbulence causes a discrete distribution of the attack angle. As the wind speed increases with height, the valley becomes relatively open and the influence of the terrain gradually decreases; thus, the extreme wind attack angle values decrease, and the distribution interval shortens.  
Figure 11: Distribution of maximum wind speed per month.  
Figure 10: Wind speed waterfall diagram: **(a)** 14 November 2017 (autumn); **(b)** 27 February 2018 (winter); **(c)** 29 April 2018 (spring); **(d)** 22 July 2018 (summer).  
From Figure 12, the mathematical expectation of the wind attack angle tends to move in a negative direction with increasing height. This phenomenon is particularly evident at altitudes between 120 and 200 m. In summary, negative attack angles at the observation point occurred more frequently than positive attack angle attacks, which is caused by the observation point being located downstream of the main incoming wind direction of the horn terrain, i.e., on the leeward side.  
The frequency distribution of the wind attack angle at a 30 m altitude is shown in Figure 13. The figure shows that the main distribution interval of wind attack angle is \(-6^{\circ}\) to \(+6^{\circ}\). There are significantly more negative wind attack angle values than positive values, and the range of wind attack angle with the highest frequency is \(-3^{\circ}\) to \(0^{\circ}\). The statistical mean of probability for the wind attack angle sample is \(-1.46^{\circ}\) with a standard deviation of 3.03. The frequency distribution of the wind attack angle is not normally distributed.