Nedeleg Bigi PhD Researcher ENSTA Bretagne 2 rue Francois Verny
29200 Brest France
nedeleg.bigi@ensta-bretagne.org www.ensta-bretagne.fr
A Quasi-Analytical 3D Kite Tether Model
Nedeleg Bigi1, Alain Nême1, Kostia Roncin1, Jean-Baptiste Leroux1, Guilhem Bles1, Christian Jochum1, Yves Parlier2
1ENSTA Bretagne 2beyond the sea R
This work is part of the beyond the sea R research
pro-gram leaded by the LBMS laboratory of ENSTA Bretagne. The whole project attempts to develop tethered kite sys-tems as an auxiliary propulsion device for merchant ship. One of the main unsolved issue unsolved concerns ship-kite mechanical interactions.
In order to model these interactions, the priority is to characterize the tether behavior. A first step is to develop a method dedicated to solve any static flight equilibrium of the kite and the tether system. Consequently, taking into account the wind gradient effect, a model based on the catenary model is proposed. This model has been de-veloped both in position and force formulations. Aerody-namic load on the tether is assumed to be constant along the tether. Furthermore, the kite is considered in a static flight with a constant lift-to-drag-ratio.
For a given kite position, the position formulation al-lows to predict the tether shape and all forces within the tether. Coupled with the kite model, this formulation is useful to obtain the whole static flight solution domain. Therefore, the flight window’s edge is defined and is com-pared with the flight window’s edge obtained with a sin-gle rigid bar tether model (cf. Figure 1). Moreover, tether forces at the kite location and at the attachment point are also compared. Significant differences are shown and demonstrate the relevancy of this model.
By contrast to the position formulation, the force formu-lation is fully analytical. Providing the tether forces, the
kite location is obtained. Assuming the aerodynamic load on the tether is negligible compared to its weight, the minimum wind velocity at kite location which allows a downwind static flight is expressed with a very simple for-mula. Coupled with the wind gradient model, the corre-sponding wind velocity at the measurement altitude (cur-rently 10 m) is obtained. Then, using this methodology, the existence of an optimal tether length to fly with a min-imum wind velocity is demonstrated.
x[m ]× 10 2 −3 −2 −1 0 1 2 y [m] ×102 −2 −1 0 1 2 3 z [m ] × 10 2 −1 0 1 2 3 4 x0 y0 z0 VS= 7.5m/s VAW
Rigid Bar Tether Model 3D Catenary Tether Model
Flight window’s edge obtained with the 3D catenary tether model (blue line) compared to the flight window’s edge obtained with a single rigid bar model (black dashed line).
