Nonlinear six-degree-of-freedom aircraft trim

When computing numerical trim solutions, it is difficult to know if all possible trim solutions have been 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 fixed 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 fixed set of values of these four parameters. The advantage of these closed-form computations, over more numerical methods, is that they give all possible solutions values.