# Estimation of Aircraft-Dependent Bumpiness Severity in Turbulent Flight
## 3 Experiments and Analysis
### Analysis of Vertical Acceleration Response  
#### 3.2.1 Instantaneous Acceleration Response  
Since accurate vertical acceleration response is significant to severity estimation of aircraft bumpiness, the acceleration response computed by UVLM was further compared to measured acceleration data provided by Quick Access Recorder (QAR) flight data. The airborne flight data acquisition system provides hundreds of flight data in the form of time series, including flight dynamics parameters and control surface deflections. Supported by China Academy of Civil Aviation Science and Technology, QAR flight data of 880 flight segments on the same scheduled airway from Beijing Capital International Airport (ZBAA) to Guangzhou Baiyun International Airport (ZGGG) were collected. According to the QAR data, eight Wind Fields (WF) were selected and used to explore the acceleration response,  
Figure 8: Comparison of pitching moment coefficients. covering the light, moderate, and severe turbulence. The maximum and minimum vertical acceleration data of the eight Wind Fields (WF1\(\sim\)WF8) are listed in Table 2.  
The acceleration response by UVLM is compared with the linear transfer function model and recorded acceleration data. It is worth noting that the acceleration data is recorded at the gravity center of aircraft. A linear transfer function model of B737-800 aircraft was built according to the modeling method of Model-4 in ref [7]. To better understand the acceleration response mechanism in turbulence, four linear models of increasing gust excitation complexity were developed in ref [7]. Considering the gust pitching rate effects in pitching and plunge dynamics and further incorporating a quasi-steady aerodynamic model with finite lag value, the Model-4 is able to track instantaneous acceleration change with the best accuracy while the accuracy of peak response is slightly weak. The longitudinal and lateral wind components are first derived by [39]  
\[\left\{ \begin{array}{l}W_{x}=V_{Gx}-V(cosa\ cos\theta+sin\theta\ sin\alpha)\\ W_{z}=V_{Gz}-V(sin\alpha\ cos\theta-cosa\ sin\theta)\end{array} \right. \tag{19}\]  
where \(V_{Gx}\) and \(V_{Gz}\) are the ground speed components recorded in QAR flight data. According to the QAR flight data of WF5, the time series of \(W_{x}\) and \(W_{z}\) are computed and shown in Figure 9a. With the wind components as the input, both the linear model and UVLM give the response of vertical acceleration. Figure 9b shows the recorded vertical acceleration data (QAR Record), the computed vertical acceleration from the linear transfer function model (Linear Model) and UVLM, respectively. Before 90 s in WF5, the data show the aircraft was at a trimmed level flight condition. From 91.5 s, the aircraft began to experience initial turbulence, approaching the minimum acceleration near 96 s, and then reaching the maximum positive load at 96.8 s. After that, the acceleration showed a continuously decrease. In this short period, the linear model was momentarily out-of-phase once encountering sudden turbulence, while the tracking accuracy was still satisfactory. However, observations from Figure 9 suggest that both linear model and UVLM are able to follow the acceleration response in moderate turbulence, while the tracking accuracy of UVLM is better than that of the linear model. Figure 10 shows the acceleration response of the two methods in WF8. This flight data sample shows a severe aircraft pumping event, in which the vertical acceleration varied from +2.034 g to +0.413 g in 1 s. The response of the two methods tended to track the overall behavior of the recorded data. However, as far as the Linear Model is concerned, the sacrifice of peak acceleration response accuracy led to the serious deviation from recorded acceleration data. In contrast to the linear model, UVLM performed much more sensitively to severe turbulence. The tracking MSE was reduced from 0.0197 of Linear Model to 0.0081 of UVLM.