In case of a boat the wind window orientation

Two parametrical definitions of 8-shaped trajectories were introduced, one based on Wellicome & Wilkinson [12] and another one based on Argatov et al. [21] works. This definition includes two parameters for the trajectory mean position in the wind window and a third one extra for its orientation, allowing continuous variations from horizontal to vertical flight paths. The present optimization strategy differs from those Reutericyclin of Dadd [16] and Naaijen et al. [1] in several points. The present analytical kite flight modeling presented in Section 3 allowed us to speed up the kite velocity calculation compared to Dadd [16] and Naaijen et al. [1] iterative method. The influence of the wind window twist was correctly taken into account in the present modeling as explained in Section 4 since Dadd [16] and Naaijen et al. [1] and [15] orientated the wind window in a simplified manner. The trajectory orientation was introduced in the optimization process presented in Section 5 allowing continuous variations from horizontal to vertical flight paths. Moreover the three trajectory parameters (azimuth, elevation and orientation) were continuously and simultaneously optimized, whereas Naaijen et al. [15] only adjusted the trajectory azimuth and Dadd [16] chose the best trajectories through a finite set of predefined horizontal and vertical trajectories. Finally, the static flight presented in Section 3.3 was considered in the optimization process while chromatid was neglected by Dadd [16] and Naaijen et al. [1].