Mathematical Problems in Engineering

Volume 2016, Article ID 2371594, 10 pages

http://dx.doi.org/10.1155/2016/2371594

## Modeling and Simulation of China C Series Large Aircraft with Microburst

School of Automation, Beihang University (BUAA), Beijing 100191, China

Received 16 February 2016; Accepted 5 June 2016

Academic Editor: Jean-Pierre Corriou

Copyright © 2016 Jiangyun Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

To simulate and analyze a large aircraft with severe wind shear, nonlinear equations for a rigid aircraft under various wind conditions were designed. In this paper, a double-vortex-ring method is adopted to generate a three-dimensional microburst wind field. This model incorporates a flight dynamics module and three flight simulations based on various forms of nonlinear equations. In addition, four primary wind gradients are considered to compute the aerodynamic coefficients. In simulation experiments with a China C series large aircraft, equations using air-relative velocities and inertial velocities are compared and analyzed. Although the nonlinear equations derived using the air-relative velocities should be identical to those using the inertial velocities, the results show that the latter are more accurate in practice because the former bring error into the simulation when estimating the acceleration induced by the wind field.

#### 1. Introduction

In the early days of aviation, the influences of a variable wind field upon flight were generally considered to be negligible, even under atmospheric perturbations. Generally, a constant wind velocity was used to estimate the flight performance and plan a flight course. The aviation community did not pay much attention to the threat of variable wind fields until one Boeing-727 flight of Eastern Airlines crashed as a result of serious wind shear in 1975 [1]. Several aviation disasters followed this, all attributed to wind shear, which made the aviation community focus on researching wind shear and its effect on flight. According to a statistical report made by ICAO, from 1968 to 1986, aviation accidents related to weather factors accounted for 30% of the total [2]. Not long before this, the flight accident report published by NTSB showed that, during 1994 to 2003, weather-related flight accidents accounted for 21.3% of the total and half of these were attributed to wind factors [3]. It can be seen that although aeronautical technology is developing rapidly, severe weather, and especially serious wind, has always been a factor in flight accidents. Therefore, the characterization of a wind field with a serious impact on flight has to be further researched, as well as the motion of an aircraft under wind impact.

A microburst is one of the most serious wind shear fields because its short duration, small scale, and high intensity cause a series of difficulties in forecasting and detection. It starts with the vertical motion of a column downdraft, which is easily caused by thunderstorm and convective activities. This vertical motion then diverges horizontally close to the ground. The transient variation in wind speed and direction will decrease the performance of an aircraft and result in flight accidents. This fact is acknowledged throughout both the aviation and meteorology communities, especially during takeoff and approach stages [4]. Since the late 1970s, a series of projects such as NIMROD and JAWS have been set up to research the characterization and hazards of wind shear using actually measured data and digital flight data records [1, 5–7]. As an extension and intension of these studies, mathematical models for simulating microburst have been modified to determine the influence of each parameter extracted from wind characterization data on the flight performance. Typically, models based on fluid dynamics have been developed because of their simplicity and high precision. Among these, the doublet sheet model [8], vortex-ring model, and vortex section superposition model [9, 10] are usually adopted to construct real-time wind fields. In fact, the first two are identical in nature and have the same results, although the doublet of the first model is perpendicular to the vortex pair in the vortex-ring model. Moreover, the doublet sheet model is usually fit to theoretical research because of the heavy burden of computing its integral operations. However, the third one is merely an approximation of the vortex-ring model. In summary, a double-vortex-ring algorithm based on the vortex-ring model, according to [4], will be chosen to establish the wind field in this paper.

Regarding the motion equations for an aircraft under a wind field, Etkin [11] first considered a constant wind velocity and derived equations in different coordinates. However, the deviation of an aircraft’s motion under a constant wind field can easily be modified, which is impossible under variable wind. Thus, Frost and Bowles [12] derived equations in detail under a variable wind field using air-relative velocities. Compared to those without disturbance, their equations incorporated the terms of the wind velocity vector and its derivative. They also compared the different forms of wind terms between different coordinates. In addition, they applied their equations to compute the response of an aircraft under wind and establish flight simulators with a wind effect module [1]. It is remarkable that the absolute derivative of the wind velocity vector, which was called the effective force multiplied by the mass of an aircraft in their thesis, was attributed to using air-relative velocities to derive the force equations. It is identical to the acceleration induced by the relative motion of the air flow to the inertial coordinates.

Moreover, a wind field can have a serious impact on flight dynamics when the acceleration induced by wind movement has the same order of magnitude as the gravitational acceleration [12]. Yuan et al. [13] presented a tracker to minimize the effect of wind on the impact-point prediction (IPP) performance. There is no doubt that all of this work laid the foundation for research on the motion characterization of large vehicles under a wind field. Furthermore, Rauw derived the force equations, under a wind field, for the airspeed, incidence, and sideslip angle according to the relationship between the airspeed and air-relative velocity vector [14]. Some scholars recommend this kind of force equation, especially when variables like the derivative of the incidence are included in the aerodynamic model.

In conclusion, many researchers prefer the equations derived using air-relative velocities for two reasons: the aerodynamic forces are defined relative to the air flow and it is convenient to explain the effect of wind velocity intuitively. Actually, the equations derived using the inertial velocities incorporate the impact of the wind velocity when computing the aerodynamic coefficients. The changes in the aerodynamic forces are equal to the forces generated by the wind velocity, and the changes in the aerodynamic moments are equivalent to the rotational motion induced by wind gradients. In theory, both forms of equations are the same since they both obey Newton’s second law. However, the practical consequences are usually unpredictable. In [1], the author regarded the kind of equations to be chosen as an individual preference.

Therefore, the different forms of the motion equations for a rigid aircraft under a wind field are first reviewed in this paper. Next, we explain the influence of wind gradients upon the angular rates and motion of an aircraft. Then, a microburst wind field is built according to [4, 15] and included in setting up a simulation platform. The results of experiments are used to explain the differences between the wind influence mechanisms in the two forms of equations.

#### 2. Modeling of Large Aircraft under Wind Field

##### 2.1. Motion Equations of Large Aircraft under Wind Field

In this paper, the North-East-Down axis system is regarded as an inertial reference frame, and all the equations are derived using body coordinates. In addition, six degree of freedom motion equations under a wind field are developed on the basis of the following four hypotheses: First, the earth is flat and has no rotation. Second, the aircraft is regarded as a rigid body and its mass is constant. Third, the wind field is called a “Taylor Frozen Field,” so it is constant with respect to time. Last, the aircraft body, including both its geometric profile and built-in mass distribution, is symmetrical about the plane, so .

###### 2.1.1. Nonlinear Equations without Perturbations

Typically, the forces acting on an aircraft primarily include the lift , drag , side force , gravity , and thrust , which have the directions shown in Figure 1. Among these, the lift, drag, and side forces are called aerodynamic forces because they are caused by the motion of the aircraft relative to the air flow. Thus, their directions are defined in accordance with the direction of the air-relative velocity vector and generally computed in the air coordinates frame. In general, thrust is regarded as acting in the symmetric plane of the rigid aircraft with an inclination denoted by .