# Estimation of Stability Parameters for Wide Body Aircraft Using Computational Techniques
## 1 Introduction
TORNADO is a program based on potential flow theory that incorporates the vortex lattice method as its background theory. The wake from lifting surfaces creates vortices and TORNADO captures these effects through horse-shoe or horse-sling arrangements. This program determines the first-order derivatives using a central-difference calculation with the help of a pre-selected state and a disturbed state. The results obtained are accurate only for small rotations or small angles of attack. Moreover, compressibility effects are also not catered to in TORNADO; hence, high Mach number situations cannot be handled accurately [12]. Athena Vortex Lattice (AVL) was developed for the MIT Athena TODOR aero software collection. AVL also solves potential flow through the vortex lattice method. It assumes quasi-steady flow and the compressibility effects are provided through the Prandtl-Gluert model. This program was designed for thin airfoils, small angles of attack, and sideslip. Since slender body analysis is not accurate, it is often suggested to leave fuselage out of  
Figure 1: The evolution of aerodynamic flow models [3; 10; 11]. the analysis in AVL [13]. Panel Aerodynamics (PANAIR) is a program that uses a higher-order panel method to predict boundary value problems using Prandtl-Gluert relations. It provides a higher-order modeling capability in subsonic and supersonic regions. PANAIR revolutionized the supersonic surface modeling in contrast to average surface meshes. The higher-order panel method yields accurate velocity distributions. PANAIR cannot predict flow dominated by viscous and transonic flow effects. Automatic wake determination through PANAIR is also not accurate. Moreover, for configurations with different total pressures, this program cannot accurately predict the flow characteristics [14]. FLUENT and CFX are two modules of ANSYS. FLUENT employs a cell-centered method and CFX works on a vertex-centered approach. This software can handle different types of meshing operations. such as polyhedral and cut cell meshing (in the case of FLUENT) and tetra and hexa mesh topologies (in the case of CFX). ANSYS is an excellent tool to determine stability and control characteristics, but it takes a long time and has a complex mesh generation process. For industry, it is an ideal tool, since its accuracy and precision is comparable to wind tunnel testing. Aerodynamic Model Builder (AMB) is a module dedicated to stability and control of the aircraft. It is used to estimate the aerodynamic forces and moments [15; 16]. Unlike DATCOM, aerodynamic analysis can be performed in TORNADO software. Moreover, compressible and non-viscous flows can be solved using EDGE (CFD solver) for an irregularly structured tetrahedral mesh produced by the mesh generators SUMO and Tetgen [15]. The feasibility of hypersonic flight is highly dependent on the controller's design. Due to extreme flow conditions, it is a challenge to develop a design for a large flight envelope and strong interactions between propulsion and structural systems [17; 18]. However, the control-oriented model, truth model, wing-cone model, curve-fitted model, and re-entry motion are few techniques with which to take up this challenge [17]. The aerodynamic stall is an important phenomenon while determining the stability and control characteristics [19; 20]. Beyond this point, non-linearities and instabilities appear in the flow, and analysis models must be accurate to comment on the complicated flow field. Bifurcation analysis is a tool that discusses the effect of unknown pitch damping dynamics when the aircraft is under a deep-stall transition [21]. Another approach to study the instability effects in time-domain methods is the recursive least squares. The technique uses a recursive formulation to account for residuals, encountered during estimation of aircraft parameters [22; 23]. The flow phenomenon over the control surfaces or wing may undergo large variations; therefore, precise simulations are required to obtain accurate results [20; 24].