Linear and nonlinear simulations of aircraft dynamics using body axis system

Abstract

PurposeThe purpose of this paper is to present a comparison of nonlinear and linear simulations of aircraft dynamics to determine the divergence of the linear solution from the nonlinear solution.Design/methodology/approachThe general equations of motion of a transport aircraft are presented both in nonlinear and linear form. The nonlinear equations are solved by using the Runge Kutta method. Linear equations are solved numerically by using the Runge Kutta method and they are also solved exactly by using the Laplace transformation method. All of these solutions are obtained by using the body axis system. The results of the simulations are plotted for different control deflections.FindingsSolution of linear equations by both methods gave the same results as expected. There are important differences in amplitude and frequency of oscillations which are obtained by using nonlinear and linear equations. These differences increase with growing input control deflection. Therefore, it is appropriate to prefer nonlinear approach to obtain more satisfactory results.Research limitations/implicationsAccurate determination of the aerodynamic derivatives is important for the accuracy of the nonlinear solutions.Originality/valueMany classical approaches use stability axis system for the solution of linear equations. However, in this paper transfer functions of the aircraft are redefined in the body axis system, because stability axes change with angle of attack and some of the stability derivatives need to be re‐evaluated for each angle of attack. Moreover, in addition to classical text book, linear equations are also solved by using the 4th order Runge Kutta medhod.