# 晴空湍流对飞机的影响分析Analysis of Influence of Clear Air Turbulence on Aircraft

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It is very difficult for civil aviation aircraft to predict CAT (clear air turbulence), since the precipitation of CAT is lower than that of the convective turbulence. So CAT is a major hidden danger affecting aviation safety. In order to detect CAT as effectively as possible, firstly, the influence of CAT on the aircraft is analyzed in this paper, and a reactive CAT detection method is researched. This method is estimating the Eddy Dissipation Rate (EDR) based on the aircraft's vertical acceleration to quantify the CAT intensity. Then, the detection process is obtained. Secondly, The Radio Technical Commission for Aeronautics revised the specification of airborne weather radar detection turbulence, in which the vertical load factor is defined as the detection amount. The relationship between the EDR and the vertical load factor can be further analyzed in detail to conclude that the impact of the CAT on the aircraft can be quantified as the vertical load factor. Finally, the conclusion of the above theoretical analysis is verified to be correct, as the EDR is calculated using the real ADS-B (Automatic Dependent Surveillance-Broadcast) data which come from a flight that has encountered CAT. Furthermore, it is proved that the CAT detection method based on the vertical load factor is reasonable, and airborne weather radars can predict CAT more accurately and reasonably by using this method. The analysis of the impact of clear-air turbulence on the aircraft has practical significance for the accurate prediction and detection of clear-air turbulence.

1. 引言

2. 基于飞机垂直加速度的EDR估计

2.1. 基本思想

$\epsilon =B{\sigma }_{T}^{3}{V}^{-1}$ (1)

2.2. 飞机响应因子

$B$ 是特定飞机的响应因子，取决于飞机特性(机翼面积，飞机质量等)和飞行条件(真空速，飞行高度等) [8] 。

${H}_{rg}\left(\omega \right)=\frac{\stackrel{¨}{z}}{{w}_{g0}}=-{\omega }^{2}\frac{-\frac{1}{2}\rho V{S}_{W}a}{-{\omega }^{2}m+i\omega \frac{1}{2}\rho V{S}_{W}a}$ (2)

$B=1/\left[{0.7}^{3/2}{I}^{3/2}\right]$ (3)

$I=\int {|{H}_{\text{r}g}\left(\omega \right)|}^{2}{\omega }^{-5/3}\text{d}\omega$ (4)

2.3. 基于ADS-B数据估计 ${\sigma }_{T}$

$\frac{\text{d}z}{\text{d}t}={v}_{z}$ (5)

$\frac{\text{d}{v}_{z}}{\text{d}t}={a}_{z}$ (6)

Table 1. Categorization of turbulence intensity

Figure 1. Calculation flowchart of EDR based on aircraft vertical acceleration

3. CAT对飞机的影响量化

3.1. 基于垂直载荷因子的晴空湍流检测方法的基本思想

${\stackrel{^}{\sigma }}_{\Delta n}=\frac{{\sigma }_{\Delta n}}{unit{\sigma }_{w}}\frac{{\left[{\stackrel{¯}{M}}_{2}\left(x\right)\right]}^{0.5}}{\frac{\sqrt{{\sigma }_{v}^{2}\left(r\right)}}{\sigma }}$ (7)

3.2. 垂直载荷因子与EDR的关系

4. 验证和分析

Figure 2. The actual flight altitude and ground speed of the aircraft

Figure 3. Partial enlarged view of the flight altitude of the aircraft

Figure 4. The vertical speed of the aircraft

Figure 5. The vertical acceleration of the aircraft

Figure 6. Standard deviation of vertical acceleration of the aircraft, T = 10

Figure 7. The power density function of ${|H\left(\omega \right)|}^{2}{\omega }^{-5/3}$

Figure 8. The power density function of ${|H\left(\omega \right)|}^{2}$

5. 结论

Figure 9. EDR estimate, T = 10 s

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