# Estimation of Aircraft-Dependent Bumpiness Severity in Turbulent Flight
###### Abstract
When it comes to the aircraft-dependent indicator of turbulence intensity, there are the Vertical Acceleration (VA) [11] and the Derived Equivalent Vertical Gust velocity (DEVG) [12]. Both of the indicators are based on the recorded in-situ vertical acceleration data. RMS-g, the Root Mean Square of vertical acceleration divided by 1-g, is a commonly used VA indicator [13]. Since different aircraft in the identical turbulence field would experience different acceleration response, the directly measured RMS-g only reflects the bumpiness severity of in-situ aircraft and cannot be applied to other aircraft without transition. In addition, the improved DEVG, although with airspeed and aircraft mass considered, is still not a satisfactory aircraft-dependent indicator of bumpiness severity [14]. Another potential problem is that these acceleration-based indicators are easily affected by aircraft control surface deflections in flight, leading to aircraft maneuvers, which also induce the acceleration changes. In order to estimate the bumpiness severity of specific aircraft, it is fundamental to build an accurate response model from vertical acceleration to turbulence. It is the longitudinal and vertical components of turbulence that mainly lead to the plunge and pitching motion of aircraft. The Vortex Lattice Method (VLM), which is a common method for analyzing aerodynamic performance of lifting body, can be used to obtain the plunge and pitching motion in turbulent flight. By assigning the horseshoe vortices on the lifting surface, the lifting body is simplified to be a flat surface, forming a planar VLM. As a technical improvement, the non-planar vortex lattices are assigned on the mean camber surface of the lifting body, while the horseshoe vortices are substituted by vortex rings to get more accurate solutions [15]. In aerodynamic performance analysis of small angle of attack circumstances, the VLM is much more efficient compared to the general compute dynamics method, which needs to solve the Navier-Stokes Equations. In recent years, VLM has been widely applied in the design of wind turbine [16], flying wing and flapping wing aerial vehicle [17; 18], the optimization of winglet [19], swept wing [20; 21], and gust wind response analysis [22]. In some special applications, including the aerodynamic analysis in aerial refueling formation flight [23; 24; 25] and innovative flap design [26], VLM shows the superior performance of rapid trial-and-error. The Unsteady Vortex Lattice Method (UVLM) is developed to get more accurate solutions because the vortex distribution and wake vortex change induced by unsteady motion of aircraft are considered [20; 21; 27]. When it comes to the gust response analysis, NASA developed wind shear coefficients based on steady VLM [28; 29]. The longitudinal aerodynamic effects induced by wind shear were computed by VLM and added to quasi-static aerodynamic model. Since the rapid-changing turbulent wind is different from low-frequency wind shear, the steady VLM lacks enough accuracy in computing aerodynamic force in turbulence. Instead, if the turbulence-effected aerodynamic performance is obtained by UVLM, a more accurate vertical acceleration response can be acquired, which forms a better basis to obtain an aircraft-dependent bumpiness severity estimation. In this paper, a method of estimating aircraft-dependent bumpiness severity in turbulent flight is explored with in-situ EDR value provided. The intensity of turbulence is first obtained according to the [PERSON] and Kolmogorov turbulence theory. With the generated time series of turbulence as the excitation, the continuous change of vertical acceleration in turbulent flight is computed based on UVLM. After that, an aircraft-dependent bumpiness severity indicator is computed by Welch spectrum estimation. Compared with the recorded vertical acceleration in flight data, the acceleration response in turbulent flight is deeply analyzed.