A Flight-Mechanics Solver for Aircraft Inverse Simulations and Application to 3D Mirage-III Maneuver

TL;DR

This paper introduces a mathematical model and numerical algorithm for inverse flight simulation of fixed-wing aircraft, demonstrated through a 3D maneuver of the Mirage-III fighter, enabling control variable computation for prescribed trajectories.

Contribution

The paper presents a novel explicit numerical algorithm for inverse simulation of arbitrary fixed-wing aircraft maneuvers, including a practical application to Mirage-III aircraft.

Findings

Successfully computed control inputs for a Mirage-III roll maneuver

Validated the model's ability to replicate prescribed aircraft trajectories

Demonstrated the method's applicability to complex 3D maneuvers

Abstract

The main objective of this paper is to present a general mathematical model and an associated numerical algorithm applicable to an arbitrary fixed-wing fixed-mass aircraft undergoing an arbitrary maneuver, based on the 3D nonlinear coupled differential-algebraic equations of motion, including force, moment, kinematic and constraint equations. The model is formulated to address the inverse simulation problem where a target maneuver is prescribed and the corresponding time dependent patterns of the control variables are solved for to meet this maneuver. The model utilizes two different moving frames of references, namely the body axes and the wind axes. The numerical algorithm features sequential solution of equations in a fully explicit manner. It is straightforward to use the model in a reverse mode, namely the direct simulation problem. The inverse problem may be summarized as follows: Inputs: Time history of desired-trajectory rectangular coordinates relative to the ground-fixed axes. A constraint should be specified, which we arbitrarily chose it to be the bank angle. Also, certain geometric and aerodynamic aircraft data are needed. Outputs: Time history of the control variables (thrust magnitude, elevator angle, rudder angle, ailerons angle), which will satisfy the aimed trajectory. The paper finally applies the presented numerical algorithm to a roll maneuver for the Mirage-III fighter.