# Estimation of Aircraft-Dependent Bumpiness Severity in Turbulent Flight
###### Abstract  
Atmospheric turbulence threatens flight safety of civil aviation aircraft by inducing aircraft bumpiness. A severity estimation method of aircraft bumpiness in turbulent flight is explored according to in-situ Eddy Dissipation Rate (EDR) indicator. With the turbulence intensity derived from EDR value, a time series of longitudinal and vertical turbulence was generated according to [PERSON] turbulence model. In order to obtain the vertical acceleration response of aircraft, the continuous change of aerodynamic force on the assembly of wing and horizontal tail was computed by Unsteady Vortex Lattice Method (UVLM). The computing accuracy was improved by using semicircle division and assigning the vortex rings on the mean camber surface. Furthermore, the adverse effects of control surface deflections on bumpiness severity estimation can be effectively removed by separating turbulence-induced and aircraft maneuvers-induced aerodynamic force change. After that, the variance of vertical acceleration, as the severity indicator of aircraft bumpiness, was obtained by Welch spectrum estimation. With the refined grid level, the pitching moment change due to control surface deflections can be solved accurately by UVLM. The instantaneous acceleration change obtained by UVLM approximates recorded acceleration data with better accuracy than linear transfer function model. A further test with a set of flight data on the same airway shows that compared with in-situ EDR indicator, the proposed method gives an aircraft-dependent estimation of bumpiness severity, which can not only be used to estimate in-situ bumpiness but also be applied to forecast the bumpiness severity of other different aircrafts. aircraft bumpiness; turbulence; vertical acceleration; spectrum estimation; unsteady vortex lattice method +
Footnote †: journal: Applied Sciences  
**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. **Key words:** aircraft bumpiness; turbulence; vertical acceleration; spectrum estimation; unsteady vortex lattice method +
Footnote †: journal: Applied Sciences  
The National Center for Atmospheric Research (NCAR) proposed the vertical acceleration-based and vertical wind-based EDR estimation method successively [5], providing routine and quantitative measurements of turbulence intensity. The vertical acceleration-based EDR algorithm, retrieving the turbulence intensity from the vertical acceleration response of aircraft, was put forward much earlier than the wind-based method [3]. Polynomial fitting function or linear transfer function was used to describe the vertical acceleration response to the turbulence [6; 7; 8]. With vertical turbulence as the single excitation, there are difficulties in describing the acceleration response with enough accuracy because both functions are derived by small perturbation approximation. On the contrary, derived by maximum-likelihood estimation, the vertical wind-based EDR indicator is obtained by directly comparing the estimated vertical turbulence with theoretical turbulence model in frequency domain. The refined vertical wind-based algorithm only requires six parameters, including the true airspeed, inertial vertical speed, left and right vane angle of attack, pitching and rolling angle, while the complex acceleration response model is exempted [9]. The World Meteorological Organization (WMO) has added the vertical wind-based EDR value in the Aircraft Meteorological Data Relay (AMDAR) [10]. However, as an aircraft-independent turbulence intensity indicator, the objective EDR value cannot provide the bumpiness severity of the specific aircraft flying through the turbulence field. Based on the EDR indication, it is necessary to obtain the bumpiness severities of different aircrafts, from a heavy long-range aircraft to a regional short-range aircraft.