## 3 Results
### Rear Fin Position Study: Axial vs. Transverse Shift of the Rear Fins  
These positions include six positions in the transverse direction (T:0-120) at a fixed axial position of A:150 and five positions in the axial direction (A:0-200) at a fixed transverse position of T:80; see Figure 7b. C\({}_{\text{L}}\): Figure 14a presents the mean lift coefficients of the 4-fin configurations versus the AoA for different transverse positions of the rear fins (T:0-120) at a fixed axial position A = 150 mm. For each configuration, the primary trend increases with increasing AoA and decreases after stall occurs similar to Figure 10a. Therefore, the reached maximum lift coefficient for T:0 and T:20 is 20% and 15% larger than that for the other configurations. In the further progress up to AoA = 45\({}^{\circ}\), C\({}_{\text{L}}\) either increases again (T:50-100), becomes almost constant (T:0-20), or further decreases (T:120). Furthermore, for T:0-50, the maximum lift coefficient is higher at larger AoAs than for other configurations T:80-120. The significant increase in C\({}_{\text{L}}\) is generated by the in-line position of the front and rear fins serving as one larger fin. Figure 14b shows the lift coefficients for different axial positions of the rear fins (A:0-200) at a fixed transverse position of 80 mm. In contrast to the variation of the transverse position, most configurations show the maximum lift coefficient at AoA = 20\({}^{\circ}\) except the configuration T:80 A:0 exhibiting the maximum C\({}_{\text{L}}\) at AoA = 25\({}^{\circ}\). Furthermore, the absolute value of the maximum C\({}_{\text{L}}\) is also very similar for all configurations. After passing the stall point, two groups occur: (1) A:0 to A:100 show a steady decrease of the mean lift coefficients until an AoA of 45\({}^{\circ}\). (2) A:150 and A:200 show an increase of the mean lift coefficient after its post-stall point decrease starting by an AoA of 35\({}^{\circ}\). C\({}_{\text{D}}\): Figure 15 presents the mean drag coefficients C\({}_{\text{D}}\) of the entire 4-fin configurations versus the AoA for different transverse positions of the rear fins (Figure 15a) and different axial positions (Figure 15b). In general, C\({}_{\text{D}}\) increases with increasing AoA similar to the mean drag coefficient of the commercial configuration, as shown in Figure 10b. Figure 13: (**a**) Mean drag coefficient of the four velocities for the entire 4-fin configuration versus the AoA and (**b**) the mean drag force of the four velocities for the entire 4-fin configuration versus the AoA. Regarding the variation of the transverse positions of the rear fins, the drag coefficient increases similarly for all transverse positions until stall occurs around AoA = 20\({}^{\circ}\). After stall, the devolutions of C\({}_{\rm D}\) deviates for different transverse positions. Therefore, the lowest drag is generated by the configurations T:80-120. This can be explained by the rear OFs being in the wake of the front fins at the AoA range of 25\({}^{\circ}\)-40\({}^{\circ}\). Figure 14: **(a)** Mean lift coefficients versus the angle of attack for six entire fin configurations. The rear fins are fixed in one axial position and shifted for six positions of the transversal direction of the surfboard. **(b)** The mean lift coefficients versus the angle of attack for five entire fin configurations. The rear fins are fixed in one transversal position and shifted for five positions of the axial direction of the surfboard. Figure 15: **(a)** Mean drag coefficients versus the angle of attack for six entire fin configurations. The rear fins are fixed in one axial position and shifted for six positions of the transversal direction of the surfboard. **(b)** Mean drag coefficients versus the angle of attack for five entire configurations. The rear fins are fixed in one transversal position and shifted for five positions of the axial direction of the surfboard. Similar behavior can be seen in Figure 15b for the variation of the axial position of the rear fins.