Nonlinear Six-Degree-of-Freedom Aircraft Trim

Abstract

Whencomputingnumerical trimsolutions,it is difŽ cult to knowifallpossible trimsolutionshavebeen found.This paper presents closed-form formulas for computing all possible trim values for six-degree-of-freedom nonlinear aircraft models. The models include gravity, nonlinear angular-rate terms, and tabular aero functions. However, the models are linear in four functions of the four inputs (thrust, aileron, elevator, rudder). The four independent control inputs lead to a four-dimensional trim set. In the subsonic case where the Mach dependence of the aero functions can be ignored, the four-dimensional trim set is parameterized by (pitch angle, roll angle, angle of attack, sideslip angle) giving at most two real trim values for each set of Ž xed values of these four parameters. When the Mach dependence of the aero functions needs to be considered, the four-dimensional trim set is parameterized by (speed, angle of attack, sideslip angle, and heading angular rate) giving up to eight trim values for each Ž xed set of values of these four parameters. The advantageof these closed-form computations,over more numerical methods, is that they give all possible solutions values.