Attainable moment sets (AMS) are a powerful method to assess aircraft controllability. However, as attainable moment sets only take into account the achievable moment set of the control effectors, they do not assess the required moment set to fulfill the aircraft mission requirements. This paper proposes to calculate a corresponding required moment set (RMS) which defines a set of moments sufficient for fulfilling aircraft controllability requirements in the mission flight envelope. The paper applies the required moment set approach to a nonlinear simulation model of an electric vertical take off vehicle (eVTOL) transition drone in hover. By comparing the required moment set to the AMS of the aircraft model, moment set margins are derived and used to assess the controllability of the considered aircraft. The results indicate that the combined evaluation directly identifies critical moment channels and margins, which is advantageous when compared to a pure AMS-based evaluation. The proposed approach enables the execution of simulation-based assessments in aircraft design and flight control development. In the early stages of aircraft design, required moment sets can support sizing, positioning and tilting of control effectors (e.g., propulsive elements) to fit the AMS to the actual required force and moment set for the specific system.

In this paper, we discuss an attainable moment set (AMS) optimization methodology considering a system’s required moment set (RMS). The AMS describes the achievable moments from a system, given its input limits. An RMS, like an AMS, is a convex set in the moment space, describing the required moments for a system to meet the designed mission profile and disturbance rejection requirements. Given the configuration of a system, its mission requirements, and the derived RMS, the proposed optimization maximizes coverage of the AMS onto the RMS, thus ensuring the system possesses the guaranteed controllability to fulfill its required missions from a design level. To achieve this goal, the variables to optimize are chosen as effector settings, such as the installation position and angle of propellers and control surfaces, which effectively change the AMS without a vast impact on major design parameters, such as mass and moment of inertia. Since the optimization includes massive geometry operations of rays intersecting polyhedron, an efficient intersection solver is proposed to speed up the optimization process. The described method is applied to an electric-vertical-take-of-landing vehicle (eVTOL) with eight hover propellers, which delivers a highly improved coverage of the RMS compared to its initial design.