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This paper addresses fundamental issues in tail-sitting and transition flight aerodynamics modeling in view of sumof-squares (SOS) algorithmic guidance and control design. A novel approach, called ϕ theory, for modeling aerodynamic forces and moments is introduced herein. It yields polynomial-like differential equations of motion that are well suited to SOS solvers for real-time algorithmic guidance and control law synthesis. The proposed ϕ theory allows for first principles model parameter identification and captures dominant dynamical features over the entire flight envelope. Furthermore, ϕ theory yields numerically stable and consistent models for 360 deg angles of attack and sideslip. Additionally, an algorithm is provided for analytically computing all feasible longitudinal flight operating points. Finally, to establish ϕ-theory validity, predicted trim points and wind-tunnel experiments are compared.

In contrast to the current overall aircraft design techniques, the design of multirotor vehicles generally consists of skill-based selection procedures or is based on pure empirical approaches. The application of a systemic approach provides better design performance and the possibility to rapidly assess the effect of changes in the requirements. This paper proposes a generic and efficient sizing methodology for electric multirotor vehicles which allows to optimize a configuration for different missions and requirements. Starting from a set of algebraic equations based on scaling laws and similarity models, the optimization problem representing the sizing can be formulated in many manners. The proposed methodology shows a significant reduction in the number of function evaluations in the optimization process due to a thorough suppression of inequality constraints when compared to initial problem formulation. The results are validated by comparison to characteristics of existing multirotors. In addition, performance predictions of these configurations are performed for different flight scenarios and payloads.