Global Singularity-Free Aerodynamic Model for Algorithmic Flight Control of Tail Sitters

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

Optimization Studies for Aircraft Considering Propeller-Wing Interaction

Environmental concerns and advances in battery technology are currently fueling a widespread growth of interest in electric aircraft. Additionally, the fundamentally different nature of electric motors, compared to combustion engines, allows designers to experiment with unconventional aircraft configurations that would otherwise be impractical. Along with providing benefits related to emissions, procurement cost, and maintenance, electric motors allow distributing propulsion on an aircraft with greater ease compared to combustion engines, which further allows taking advantage of performance benefits through propulsion integration. To design aircraft that effectively take advantage of this increased design freedom requires the ability to answer some questions that have not been addressed in previous literature. Two such questions that this dissertation focuses on, with the common theme of propeller-wing interaction, are: What does the optimal takeoff trajectory for a tilt-wing electric vertical-takeoff-and-landing aircraft look like and how do various design and performance considerations, including those related to propeller-wing interaction and wing stall, affect it? Does optimizing a wing while considering propeller effects using computational fluid dynamics provide significant aerodynamic performance benefits? The first part of this dissertation explores the design space with takeoff in mind, and the second part explores the design space with cruise in mind. For the first part, simplified models for the aerodynamics, propulsion, propeller-wing flow interaction, and flight mechanics are used to carry out gradient-based optimization studies for the takeoff-to-cruise trajectory of a tandem tilt-wing eVTOL aircraft. Results for optimizations with and without stall and acceleration constraints, with varying levels of flow augmentation from propellers, are presented and show that the optimal takeoffs involve stalling the wings or flying near the stall angle of attack. However, the results also show that the energy penalty for avoiding stall is practically negligible. Additionally, without acceleration constraints, the optimized trajectories involve rapidly transitioning to forward flight and accelerating, followed by climbing at roughly constant speed, and then accelerating to the required cruise speed. With an acceleration constraint for passenger comfort, the transition, climb, and acceleration phases are more gradual and less distinct. Results showing the impact of wing size and available power on the optimized trajectories are also presented. For the second part, the cruise drag of a wing with a tractor propeller is minimized using aerodynamic shape optimization. Reynolds-averaged Navier--Stokes computational fluid dynamics with an actuator-disk approach is used for the simulations, and a gradient-based algorithm is used for the optimization. Changing the rotation direction of the propeller, changing the spanwise location of the propeller, and optimizing the twist and airfoil shapes of the wing impact the aerodynamic performance significantly. However, optimizing the wing while considering the propeller slipstream provides little additional benefit compared to optimizing it without considering the propeller slipstream (the difference is less than one drag count). The wings optimized without considering the propeller slipstream are naturally able to recover swirl almost as effectively as the wings optimized while considering the propeller slipstream, and the propeller-induced velocities for the cruise condition are not high enough to lead to significant airfoil-shape design changes. These conclusions are reached for both inboard-mounted and tip-mounted propellers. Additionally, a simple first-principles-based analytic expression for estimating propeller-induced tangential velocities is derived.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/166109/1/sschau_1.pd