## 3 Results  
### Lift and Drag of the Commercial 4-Fin Configuration (fin Position T:80/A:150)  
**C\({}_{\text{L}}\)**. Figure 10a shows the lift coefficient as a mean of all four fins and separately for the single fins, averaged over time, as a function of the AoA for the commercial 4-fin configuration. Regarding the IFs, the lift coefficients of both increase for increasing AoA until their maximum values at AoA = 20\({}^{\circ}\). After the maximum, stall occurs and the lift coefficients decrease for both fins. As a result of this, the lift of the front IF is always larger than the lift of the rear IF due to the non-interrupted fluid flow at the front fins. In contrast, the OF fin shows different behavior. After the stall and the subsequent lift decrease, the lift coefficients rise again, reaching the maximum at AoA = 45\({}^{\circ}\). This decrease and increase of the lift coefficient is a result of the rear OF movement with increasing AoA into and out of the wake of the front OF. Furthermore, stall occurs at a smaller AoA = 15\({}^{\circ}\) at the front OF in contrast to AoA = 20\({}^{\circ}\) at the rear OF. The reason for the earlier stall at the front OF is the flat shape of the suction side of the front OF, which forces a flow separation at the leading edge of the fin. For the rear OF, the early stall does not occur because the main flow direction in this region is slightly tilted downwards by the IFs; see Figure 11a-c. This deviation of the main flow direction is also responsible for the final increase of the lift. With an increasing AoA, the main flow between IFs and OFs is tilted more downwards, which counteracts the flow separation at the rear OF. However, the larger lift decrease at the rear OF is caused by its position being fully in the wake of the front OF, which drastically reduces its effectiveness regarding the flow. Just when the rear OF moves out of the wake at AoA = 35\({}^{\circ}\), the fin is again flow passed, and lift forces are generated with a maximum at AoA = 45\({}^{\circ}\). **C\({}_{\text{D}}\)**: Figure 10b shows the drag coefficient versus the AoA as a mean value and separately for the single fins. The drag coefficients of both IF and the front OF increase steadily over the whole range of AoAs. In contrast, the rear OF shows a decrease in the AoA range between 20\({}^{\circ}\)-30\({}^{\circ}\), with a subsequent increase up to a maximum located at an AoA of 45\({}^{\circ}\). This drag decrease of the rear OF is forced by its position in the wake of the front OF accordingly to the lift forces. In this AoA range, the front OF shadows the rear OF from the main flow, which reduces C\({}_{\text{D}}\) to nearly zero. For AoA > 20\({}^{\circ}\), the recirculation areas on the fins start to separate and move downstream, similar to the 3-fin configuration [11]. A detailed description of these unsteady effects as a function of the AoA is also given in [11]. Figure 10: (**a**) Lift coefficients versus the AoA, and (**b**) drag coefficients versus the AoA for the commercial fin position (T:80/A:150). The small figures show the flow field of two AoAs. Lift and Drag for Four Different \(u_{\text{in}}\) (5 m/s, 7.5 m/s, 10 m/s, and 18 m/s) at the Commercial 4-Fin Configuration  
A series of simulations including the commercial 4-fin position (T:80 A:150) and four different velocities were executed to investigate the effects of different inflow velocity on the lift and drag coefficients of the surfboard fins. The dimensionless mean lift and drag coefficients and the corresponding mean forces are shown in Figure 12 for the four inflow velocities: 5 m/s, 7.5 m/s, 10 m/s, and 18 m/s. C\({}_{\text{L}}\) and lift force: The mean lift coefficients for the four velocities, as displayed in Figure 12a, follow the trend of the mean C\({}_{\text{L}}\) shown in Figure 10a: after an increase up to its maximum at AoA = 20\({}^{\circ}\), C\({}_{\text{L}}\) first decreases until an AoA of 35\({}^{\circ}\). Subsequently, it rises again up to an AoA = 45\({}^{\circ}\).