# Benchmark Sea Trials on a 6-Meter Boat Powered by Kite
## 5 Results
### Results Processed with Phase-Averaging Method  
The phase-averaging method, presented in Reference [21], was adapted to take into account the additional data induced by the boat. All the 101 runs are not suitable. Indeed, a minimum reproducibility of the trajectories is required, and some sailing configurations, as the manual steering, do not allow meeting this requirement. Eventually, 10 runs were selected and results are presented in Table 3. The back tether ratio \(r_{b}\) (Equation (22)) and the amplitude ratio \(r_{a}\) were already considered in Reference [21]. The amplitude ratio is the amplitude of the force divided by the averaged force value along the trajectory. In addition, two others ratio are introduced here: the propulsive ratio \(r_{prop}\) and the amplitude speed ratio \(r_{s}\). The first one denotes the part of the kite load useful for propulsion (i.e., the projection of the kite force on the \(x_{\psi}\)-axis):  
\[r_{prop}=\frac{F_{k}\cdot x_{\psi}}{F_{k}}. \tag{25}\]  
The amplitude speed ratio denotes the maximum speed variation during the kite eight pattern in comparison with the average speed:  
\[r_{s}=\frac{\text{max}(V_{s})-\text{min}(V_{s})}{\mu_{V_{s}}}=\frac{\bigtriangleup V _{s}}{\mu_{V_{s}}}. \tag{26}\]  
Figure 17: (**a**) Back tether ratio for the three kites. (**b**) Power ratio according to the true wind angle, for two different kites. Moreover, other quantities are introduced denoting the variation of some parameters for the boat, as the amplitudes of the rudder angle \(\triangle\delta_{R}\), the heading angle \(\triangle\psi\), the roll angle \(\triangle\phi_{s}\) and the amplitude of the pitch angle \(\triangle\phi_{s}\). On the kite side, the amplitude of the kite steering command \(\triangle\delta\), the amplitudes in azimuth \(\triangle\phi\) and in elevation \(\triangle\theta\) are shown in Table 3. The first three columns denote the short name of the case, the kite used and the true wind angle \(\beta_{WT}\). This parameter is very sensible. The case d04f1 is remarkable for the very low amplitude in elevation angle. This represents a turning radius of about 3 meters, which is very tight given the size of the kite and well below the limit identified by [PERSON] [3]. The force coefficient, \(C_{k}\), already used for onshore trials in Reference [21], was naturally computed here with the relative wind speed instead of the true wind speed. This parameter is very sensible. For two very close configurations (D02f5 and D02f6 in Table 3), dramatic differences are observed. Thus, the propulsion power is doubled, while at the same time, the force coefficient goes from 4.8 to 12.9. The only culprit appears to be a 15\({}^{\circ}\) change in elevation angle from 65\({}^{\circ}\) to 50\({}^{\circ}\). The speed of the boat was therefore increased by more than 26%. Another interesting thing to note is the fall of 65% in terms of the amplitude of the rudder angle, reflecting an appreciable increase in stability. Compared to onshore results, in the present study, the force coefficients recorded values were significantly lower by more than 20%. This may be explained by the fact that in the onshore campaign, all tests were conducted in \"crosswind conditions\", as called by the Airborne Wind Energy (AWE) research community (i.e., full downwind). Instead, the results presented in the Table 3 were obtained with true wind directions from the beam reach (106\({}^{\circ}\)) to the full downwind (180\({}^{\circ}\)). In line with the zero-mass model, the results showed a sharp decrease in the force coefficient as the wind angles decreased. Thus, the lowest value of 3.2 in force coefficient corresponds to the lowest wind angle (106\({}^{\circ}\)) while the highest value (12.9) corresponds to full downwind (182\({}^{\circ}\)). Force coefficient was also computed with the method presented in Section 5.3 (see Appendix A). A top value of 20 was reached in the full downwind case (d05f10), which is significantly higher (+24%) than that obtained onshore [21].