Wake Vortex Model Predicts Sharp Power Drop for Airborne Wind Energy

Integrating wake modeling into the optimal control frameworks used to simulate airborne wind energy systems substantially reduces expected power generation, according to a preprint under review for the journal Wind Energy Science. Optimal control calculations are frequently employed to predict the flight trajectories and mechanical performance of airborne wind systems, yet such numerical forecasts depend entirely on the fidelity of underlying aerodynamic models. When fluid momentum conservation and wake formation are integrated using a vortex filament approach, the model forecasts a 20 percent to 30 percent reduction in available power compared with formulations that treat induced velocity as negligible.

To evaluate these dynamics, researchers Rachel Leuthold, Jochem De Schutter, Curran Crawford, Sébastien Gros, and Moritz Diehl introduced a rigidly-convected, lifting-line vortex model into an optimal control problem. The team sought to determine how a vortex-filament representation could be incorporated along irregular flight paths that must satisfy numerous inequality constraints. The rigidly-convected lifting-line approach was selected specifically to achieve a compromise between overall computational expense and geometric modeling sensitivity.

The investigators created a solvable numerical framework by lifting selected algebraic variables directly into the decision variables of the airborne wind energy optimal control problem.

The aerodynamic estimates produced by the rigidly-convected lifting-line model showed consistency with independently published Large Eddy Simulations across different operating regimes. According to the preprint, this agreement held under rotationally steady conditions as well as during dynamic flight maneuvers, taking into account the underlying modeling assumptions.

The primary demonstration problem evaluated in the research focused on a two-kite system based on the Ampyx-AP2 architecture operating across a single-winding flight trajectory. When comparing optimization runs with wake effects against those assuming negligible induced flow, the model predicted a 20 percent to 30 percent loss in harvestable aerodynamic power. The authors noted that the exact magnitude of the observed reduction depended on the specific mathematical objective and the initialization chosen for the optimization problem.

Despite successfully converging, solving the optimal control problem with an integrated wake model required substantial computational resources. The authors reported that memory requirements scaled directly with the total number of vortex elements instantiated across the entire problem horizon. Furthermore, processor execution time scaled with more than the square of the total number of vortex elements, highlighting a steep computational penalty for higher temporal or spatial discretization.

The study also identified significant sensitivity to numerical initialization, noting that final solutions were heavily influenced by the homotopy strategy applied during the solution process. While the results demonstrate that vortex-filament wake dynamics can be successfully integrated into constrained airborne wind energy trajectory optimizations, the investigators concluded that high processor times, memory overhead, and initialization dependencies remain key limitations for routine engineering use.

Lead author Rachel Leuthold and co-author Moritz Diehl conducted the research within the Systems Control and Optimization Laboratory in the Department of Microsystems Engineering at the Albert-Ludwigs-University in Freiburg, Germany. Co-investigator Jochem De Schutter contributed from TransnetBW in Wendlingen am Neckar, Germany, while Curran Crawford collaborated from the Institute for Integrated Energy Systems at the University of Victoria in Victoria, Canada. Sébastien Gros supported the project from the Department of Engineering Cybernetics at the Norwegian University of Science and Technology in Gløshaugen, Norway.

The study, titled ‘A rigidly-convected, lifting-line vortex model in the optimal control of airborne wind energy systems,’ was formally received on November 3, 2026, and entered open public discussion on November 12, 2026, under distributed review for Wind Energy Science.

Subject of Research: Wake modeling and optimal control in airborne wind energy systems

Article Title: A rigidly-convected, lifting-line vortex model in the optimal control of airborne wind energy systems

Article References: Leuthold, R., De Schutter, J., Crawford, C., Gros, S., & Diehl, M. (2026). A rigidly-convected, lifting-line vortex model in the optimal control of airborne wind energy systems. https://doi.org/10.5194/wes-2026-211

Image Credits: AI Generated

DOI: 10.5194/wes-2026-211

Keywords: airborne wind energy, optimal control problem, wake modeling, lifting-line theory, vortex filament model, Ampyx-AP2, power loss, induced velocity, aerodynamic simulation, trajectory optimization, computational expense, Large Eddy Simulation, homotopy strategy, inequality constraints, flight dynamics, wind energy science