This paper presents a quasi-steady simulation framework for soft-wing kites with suspended control unit employed for airborne wind energy. The kites are subject to actuation-induced and aero-elastic deformation and are described by a coupled aero-structural model in a virtual wind tunnel setup. Key contributions of the present work are a kinetic dynamic relaxation algorithm and a procedure to define a physically consistent initial state. For symmetric actuation, the kite is pitch-statically stable and the simulations converge to a static equilibrium state. Most soft-wing kites are not roll-statically stable and do not find a static equilibrium without a symmetry assumption, as this introduces non-zero roll- and yaw moments. Another important contribution is the introduction of a steady circular flight state that enables convergence without a symmetry assumption. By neglecting gravity, the kite can fly in a perfectly circular turning motion around the wind vector with a constant radius and constant rotational velocity without requiring active control input. In an idealized wind-aligned tether case, the difference in aerodynamic- and centrifugal force application centers makes it impossible to achieve both a force- and moment equilibrium. This was resolved by including an elevation angle that introduces a radial tether force component, which introduces a centrifugal and aerodynamic force difference. Therefore, an operating point with roll equilibrium can be found where the kite finds a static equilibrium, enabling the first quasi-steady simulations of turning flights. Simulated quantifications of soft-wing kite turning behavior, i.e., turning laws, contribute to better kite- and control design.

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Airborne wind energy systems using flexible membrane wings have the advantages of a low weight, small packing volume, high mobility and rapid deployability. This paper investigates the aero-structural deformation of a leading edge inflatable kite for airborne wind energy harvesting. In the first step, a triangular two-plate representation of the wing is introduced, leading to an analytical description of the wing geometry depending on the symmetric actuation state. In the second step, this geometric constraint-based model is refined to a multi-segment wing representation using a particle system approach. Each wing segment consists of four point masses kept at a constant distance along the tubular frame by linear spring-damper elements. An empirical correlation is used to model the billowing of the wing’s trailing edge. The linear spring-damper elements also the model line segments of the bridle line system, with each connecting two point masses. Three line segments can also be connected by a pulley model. The aerodynamic force acting on each wing segment is determined individually using the lift equation with a constant lift coefficient. The particle system model can predict the symmetric deformation of the wing in response to a symmetric actuation of the bridle lines used for depowering the kite (i.e., changing the pitch angle). The model also reproduces the typical twist deformation of the wing in response to an asymmetric line actuation used for steering the kite. The simulated wing geometries are compared with photogrammetric information taken by the onboard video camera of the kite control unit, focusing on the wing during flight. The results demonstrate that a particle system model can accurately predict the geometry of a soft wing at a low computational cost, making it an ideal structural building block for the next generation of soft wing kite models.@en