2D Aircraft Trim

The purpose of this document is to discuss a 2-dimensional trim model for an aircraft along with the necessary mathematical methods to solve the problem, the computer implementation of the method and the results. The aircraft is climbing at a constant translational velocity, i.e. the aircraft is not accelerating. The 2-dimensional simplification; restricting the motion of the aircraft to longitudinal motions only; is made possible by assuming the sideslip is zero, the aircraft is symmetric and the aircraft is climbing at an angle, γ. Given the aircraft geometry and flight conditions, the aerodynamic forces and moments acting on the aircraft can be computed using the Aero-F computer program (Ref. [2], Ref. [3] & Ref. [4]). It is important to note that the output of the Aero-F program is defined in a reference frame where the origin is not at the center of gravity; thus the Aero-F reference frame is clearly defined below, in order for use in the development of the trim model. Then the equations for the longitudinal forces and moments on the aircraft are developed, resulting in a system of 3 equations with 3 unknowns. The system will be solved using the iterative Newton's method for systems of equations, which is also presented below. After the trim problem has been motivated and a method for solving it has been outlined, the computer implementation of the problem is thoroughly discussed; including the interactions of the Aero-F program with the trim program, the user interactions with the input files and the output of the programs. Some of the nice features of the trim program are as follows: it allows the user to specify a rigid or an elastic aircraft, it allows the user to choose whether or not to compute the derivatives at every iteration, and the user can specify how many unknowns to solve for. After the computer implementation is presented, the results are discussed; showing clearly that both rigid and aeroelastic computations yield similar results whether or not the derivative is recomputed.