## 1 Introduction
However, it is still lack of enough accuracy to describe the acceleration response. To further explore the modeling accuracy, four linear-transfer function models reflecting aircraft's plunge and pitching motion in turbulence were developed, with quasi-static aerodynamic model and controls fixed assumptions [12]. These models were tested, respectively and compared with the recorded acceleration data on Boeing 757 aircraft. In ref [13], real-time turbulent wind effects during aerial refueling were studied. Based on Dryden turbulence model assumption, turbulence parameters were identified. By feeding the identified turbulence into flight dynamics model, the simulation results and recorded data are compared. In ref [14], to study the riding comfort in turbulence, acceleration responses in different seating locations were studied by dynamic simulation. The above studies show that there are major differences between measured and theoretical responses To summarize, the linear-transfer function or fitting function cannot accurately describe the acceleration response of aircraft in turbulence. Since EDR algorithm accuracy can easily be affected by control-surface deflection [15], another significant disadvantage is that with controls fixed assumption and only vertical wind as the excitation, these methods cannot distinguish the acceleration change caused by aircraft maneuvering or turbulence. In order to obtain real turbulence severity in a vertical acceleration-based EDR algorithm, the effect of maneuvering flight on vertical acceleration must be eliminated. As an effective way of aerodynamic analysis and optimization, vortex lattice method (VLM) can be used to obtain the turbulence-effected vertical acceleration response. In earlier studies, planar VLM was adopted by assigning horseshoe vortices on lifting surface. In recent years, nonplanar vortex lattices are assigned on mean camber surface and vortex rings are formulated to obtain more accurate solutions [16]. Although aerodynamic characteristics can be analyzed accurately by compute fluid dynamics method, VLM is still a popular and rapid medium-accurate computing method. VLM has been widely used in aero-elastic analysis [17], wind turbine design [18], lift and induced drag computation [19], wing design optimization [20] and gust wind response analysis [21]. When it comes to the aero-elasticity and gust wind analysis, the influence of aircraft motion and wake on aerodynamic performance must be considered. Unsteady vortex lattice method (UVLM) is used to solve these problems [17; 19; 20]. In some special applications, like aerodynamic analysis in aerial refueling formation flight [22; 23; 24] and innovative flap design [25], VLM possesses the advantage of rapid trial-and-error. NASA has developed wind shear coefficients based on steady VLM [26; 27]. With no-sideslip assumption, additional aerodynamic effects induced by shear wind were computed and added to quasi-static aerodynamic model. With the simplified combination of wing and horizontal tail, satisfactory accuracy was obtained by VLM in shear wind. However, steady VLM is not suitable for computing aerodynamic force in high frequency turbulent wind. If the turbulence-effected aerodynamic performance is obtained by unsteady VLM, a more accurate vertical acceleration response can surely be acquired, which will be beneficial to vertical acceleration-based EDR algorithm. In this study, a method for computing aircraft's vertical acceleration response in turbulence is proposed. Based on nonplanar and unsteady vortex ring method (VRM), the continuous change of aerodynamic force in turbulent flight will be computed. Furthermore, an acceleration-based EDR algorithm will be developed to estimate the turbulence severity. For a specific wing, the computing results based on VRM will be verified by wind tunnel test data and aircraft-modeling data. After this, aerodynamic force and acceleration changes in turbulent flight will be analyzed.