## 4 Discussion
### Rear Fin Position Study: Axial vs. Transverse Shift of the Rear Fins  
Moving the rear fins in the transverse direction from the rail to the longitudinal axis of the surfboard implicate that:  
1. The stall point is moving from an AoA of 30\({}^{\circ}\) (T:0) to 20\({}^{\circ}\) (T:120),
2. the maximum of the lift coefficients decreases significantly from 0.87 (T:0) to approx. 0.7 (T:50-120), and
3. the lift coefficients also decrease in the range of high AoA of 30\({}^{\circ}\)-45\({}^{\circ}\).  
We assume that, at T:0 and T:20, the front and the rear fin of each side (outside and inside) act as one large fin. Therefore, these configurations can be seen as a two-fin configuration and therefore produce a higher lift force owing to the increased fin area (sum of front and rear fin at both rails). The corresponding stall points are located at AoA = 25\({}^{\circ}\) and 30\({}^{\circ}\), which are higher compared to the positions of T > 20. Therefore, these two configurations can be surfied with greater stability up to a higher AoA before force fluctuations occur for positions T > 20. Furthermore, the rear OF is not shadowed by the front OF for AoAs up to 20\({}^{\circ}\), as shown in Figures 10a and 11.  
Moving the rear fins in the axial direction toward the tail of the surfboard implicate that:1. The stall point is moving from an AoA of 25\({}^{\circ}\) (A:0) to 20\({}^{\circ}\) (A:50-200),
2. the maximum lift coefficient decreases slightly from 0.72 (A:0) to 0.69 (A:50-200), and
3. the lift coefficients start to increase again at an AoA = 35\({}^{\circ}\) for the positions A:150 and A:200.  
The rear fins at A:200, which is the position nearest to the tail, especially the rear OF, are not significantly disturbed by the wake of the front fins like in other fin configurations. Therefore, this configuration has no massive decrease in lift and can produce a high, nearly constant, lift coefficient at high AoA > 20\({}^{\circ}\) after stall occurs. However, on the other hand, position A:200 produces the highest drag coefficient at high AoAs. These two effects indicate a stable surfing condition due to the high lift and a constant lift force gradient but with a tendency to result in a more significant speed loss. Thus, the maneuverability and direction control may be more challenging. These findings in fin positioning support our Hypothesis 3.  
Furthermore, we suppose that if a shaper wants to create a 4-fin configuration at the surfboard that produces a high lift coefficient, one has to place the rear fins in flow direction behind the front fins, which generally corresponds to a position near the rails of the surfboard like position T:0 A:150 and T:20 A:150. If a shaper wants to have a high lift coefficient at high AoA, one has to place the rear fins near the tail of the surfboard like the positions T:80 A:200 or T:50 A:150. We also suppose that if a shaper wants to create a radical 4-fin configuration at his surfboard, which produces a low drag coefficient over the whole range of AoA, one has to place the rear fins at positions T:120 A:150 or T:80 A:100. If the shaper wants to set up a 4-fin configuration with a steadily increasing drag coefficient, one has to place the fins at positions T:50 A:150 or T:80 A:200. If a shaper wants to set up a 4-fin configuration with a high lift-to-drag ratio at an AoA of 5\({}^{\circ}\), one has to choose the positions of T:80-120 A:150 or T:80 A:100-200.