Kite Flight Simulators Based on Minimal Coordinate Formulations

Gonzalo Sánchez-Arriaga Ramón y Cajal Research Fellow Universidad Carlos III de Madrid Bioengineering and Aerospace

Engineering Department Avda. de la Universidad 30 28911 Leganés (Madrid) Spain gonzalo.sanchez@uc3m.es www.aero.uc3m.es

Kite Flight Simulators Based on Minimal Coordinate Formulations

Gonzalo Sánchez-Arriaga1_{, Alejandro Pastor-Rodríguez}1_{, Manolo García-Villalba}1_{, Manuel Sanjurjo-Rivo}1_,

Ricardo Borobia-Moreno1,2_{, Roland Schmehl}3 1_{Universidad Carlos III de Madrid}

2_{Spanish National Institute of Aerospace Technology (INTA)} 3_{Delft University of Technology}

Analytical mechanics techniques are applied to the con-struction of three kite flight simulators with applications to airborne wind energy generation and sport uses. All of them were developed under a minimal coordinate formu-lation approach. This choice has the main advantage of yielding a set of ordinary differential equations free of al-gebraic constraints, a feature that distinguishes the sim-ulators from codes based on classical mechanics formu-lation and improves their robustness and efficiency. The first simulator involves a kite with a flexible tether, a bridle of variable geometry, and several on-board wind turbines. Such a simulator, which models the tether by a set of rigid bars linked with ideal joints, can be used to study the on-ground generation of electrical en-ergy through yo-yo pumping maneuvers and also the on-board generation by the wind turbines. The second simu-lator models a kite linked to the ground by two rigid con-trol lines. This numerical tool is aimed at the study of the dynamics of acrobatic kites and the traction analysis of giant kites to propel cargo ships. The third and last sim-ulator of this work considers a kite with four control lines similar to the ones used in kitesurf applications. Two of them are rigid tethers of constant length that connect the leading edge of the kite with a fixed point at the ground. The other two tethers are elastic and they link a control bar with the trailing edge of the kite.

The performances of the simulators in terms of

compu-tational cost and parallelization efficiency are discussed. Their architectures and user interfaces are similar, and appropriate to carry out trade-off and optimization anal-yses for airborne wind energy generation.

1 0.8 0.6 x/L0 0.4 0.2 0 -0.8 -0.6 -0.4 -0.2 y/L0 0 0.2 0.4 0.6 0.8 0.6 0.8 0 0.2 0.4 1 z/ L0

Four-line kite simulator. References:

[1] Sánchez-Arriaga, G., García-Villalba, M., and Schmehl, R. "Modeling and dynamics of a two-line kite", Applied Mathe-matical Modelling, Vol. 47, July. 2017, pp. 473 - 486.

DOI:10.1016/j.apm.2017.03.030

[2] Pastor-Rodríguez, A., Sánchez-Arriaga, G., and Sanjurjo-Rivo, M. "Modeling and Stability Analysis of Tethered Kites at High Al-titudes", Journal of Guidance, Control, and Dynamics, May. 2017,

DOI:10.2514/1.G002550