Newton-Raphson Methods in Aircraft Trim: A Comparative Study

Abstract

While simulating and analyzing air-vehicle motion during flight, it is not possible to use the nonlinear model directly without appropriate initial conditions. The initial condition stands for a point about which air-vehicle flight condition must not change abruptly. This point is referred to as the trim condition. In this paper, classical Newton-Raphson method will be used first to find the trim conditionby solving a system of nonlinear algebraic equations. When the starting point is not close to a solution, the Newton-Raphson algorithm behaves erratically. Sometimes, components of the unknown inputs and states or the Jacobian will result in numerical instability. Global convergence is then addressed, which is the issue of trying to force convergence to a solution from a remote starting point. The Newton-Raphson method can be made more robust by using line search technique. A comparative study is carried out by incorporating different methods for solving the nonlinear equations in F-16 aircraft trim. The attainability of various trim conditions is also investigated.