The design and control of airborne wind energy systems requires fast, validated reduced-order models. Because the aerodynamic identification of soft, bridled kites is challenging, models that minimise the number of parameters to be identified can be particularly valuable. This paper presents a reduced-order model for the translational dynamics of bridled kites, consisting of a wing supported by multiple bridle lines. The kite is modelled as a point mass in a spherical reference frame aligned with the instantaneous tangential flight direction, referred to as the course reference frame. The angle of attack follows geometrically from a constant angle between the wing chord and the bridle line system, under the assumption that the wing instantaneously aligns with the pull direction, i.e. the rotational dynamics are neglected. The formulation retains gravitational and inertial terms introduced by the curvilinear reference frame and applies a quasi-steady condition of zero-path-aligned acceleration, modelling the motion as a sequence of quasi-steady (trimmed) states that relate the trim speed and angle of attack. Model validation is based on public flight datasets from two different soft-wing kites and on dynamic simulations that cover higher wing loadings. Results show that for low wing loadings typical of soft kites, the quasi-steady approximation reproduces the dynamic trajectories with less than 1 % deviation in mean reel-out power. For higher loadings and hard-wing kites, inertia introduces substantial phase lag and amplitude damping, causing power deviations of up to 14 %. Overall, the proposed model provides a computationally efficient framework for analysing the translational dynamics of bridled kites. The formulation is well suited to trajectory optimisation, parametric studies, and control design in airborne wind energy systems.

Airborne wind energy systems (AWESs) leverage the generally less variable and higher wind speeds at increased altitudes by utilizing kites, with significantly reduced material costs compared to conventional wind turbines. Energy is commonly harnessed by flying crosswind trajectories, which allow the kite to achieve speeds significantly higher than the ambient wind speed. However, the airborne nature of these systems demands active control and makes them highly sensitive to changes in wind conditions, making accurate wind measurements essential for steering the kite along its optimal trajectory. This paper presents an advanced sensor fusion technique based on an iterated extended Kalman filter (EKF) for state and wind estimation for AWESs. By integrating position, velocity, tether force, and reeling speed, this method provides accurate estimations of system dynamics, including kite orientation and tether shape. The estimates of the wind speed and direction are compared to lidar measurements, showing good agreement across various atmospheric conditions, with 10 min averaged root mean square error (RMSE) values below 1 m s−1 and 5°, respectively. The results demonstrate that this approach can effectively capture the transient dynamics of atmospheric wind using sensors typically already present in AWESs, making it suitable for supervisory control strategies and ultimately enhancing energy efficiency and system reliability across diverse atmospheric conditions.

Soft-wing kites for airborne wind-energy harvesting function as flying tensile membrane structures, each of whose shape depends on the aerodynamic load distribution and vice versa. The strong two-way coupling between shape and loading poses a complex fluid-structure interaction problem. Since computational models for such problems do not yet meet the requirements of being accurate and at the same time fast, kite designers usually work on the basis of intuition and experience, combined with extensive iterative flight testing. This paper presents a fast aero-structural model of leading-edge inflatable kites for the design phase of airborne wind-energy systems. The fluid-structure interaction solver couples two fast and modular models: a particle system model to capture the deformation of the wing and bridle-line system and a 3D nonlinear vortex step method coupled with viscous 2D airfoil polars to describe the aerodynamics. The flow solver was validated with several wing geometries and proved to be accurate and computationally inexpensive for pre-stall angles of attack. The coupled aero-structural model was validated using experimental data, showing good agreement in the deformations and aerodynamic forces. Therefore, the speed and accuracy of this model make it an excellent foundation for a kite design tool.