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Abstract
A mathematical model of a kite connected to the ground by two straight tethers of varying lengths is presented and used to study the traction force generated by kites flying in crosswind conditions. The equations of motion are obtained by using a Lagrangian formulation, which yields a loworder system of ordinary differential equations free of constraint forces. Two parameters are chosen for the analysis. The first parameter is the wind velocity. The second parameter is one of the stability derivatives of the aerodynamic model: the roll response to the sideslip angle, known also as effective dihedral. This parameter affects significantly the lateral dynamics of the kite. It has been found that when the effective dihedral is below a certain threshold, the kite follows stable periodic trajectories, and naturally flies in crosswind conditions while generating a high tension along both tethers. This result indicates that kitebased propulsion systems could operate without controlling tether lengths if kite design, including the dihedral and sweep angles, is done appropriately. If both tether lengths are varied outofphase and periodically, then kite dynamics can be very complex. The trajectories are chaotic and intermittent for values of the effective dihedral below a certain negative threshold. It is found that tether tensions can be very similar with and without tether length modulation if the parameters of the model are wellchosen. The use of the model for pure traction applications of kites is discussed.
Original language  English 

Pages (fromto)  473–486 
Journal  Applied Mathematical Modelling: simulation and computation for engineering and environmental systems 
Volume  47 
DOIs  
Publication status  Published  Jul 2017 
Keywords
 Kite control
 Kite modeling
 Lagrangian systems
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Dive into the research topics of 'Modeling and dynamics of a twoline kite'. Together they form a unique fingerprint.Projects
 1 Finished

REACH: Resource Efficient Automatic Conversion of HighAltitude Wind
Schmehl, R., Peschel, J. O. & Schelbergen, M.
1/12/15 → 31/08/19
Project: Research
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