## Materials and Methods
### Geometric Dimensions of the Fins  
The _FCS Accelerator II_ fins (_FCS_, Newport Beach, NSW/Australia) plugged on a surfboard were scanned in a computer tomograph (CT) of type SOMATOM Definition AS 64 (SIEMENS Healthineers, Forchheim, BY/GER); see Figure 4. The high-resolution CT images were post-processed with a Gaussian filter and a Marching Cubes algorithm, which generates watertight and manifold triangle meshes [40]. For obtaining just the results of the fins without the influence of a surfboard geometry, only the 3D geometries of the fins, arranged in a commercial 4-fin configuration of a _ROBERTS Surboards_ (Ventura, CA, USA) _The Dreamcatcher_ 6'8 model, were imported into STAR-CCM+; see Figure 4b.  
The cant angle of the fins within the 4-fin configuration is approximately \(8.5^{\circ}\); see Figure 5a. The Toe-In angle is approx. \(3.5^{\circ}\); see Figure 5a. The _FCS Accelerator II_ fins have an asymmetric shape with a flat inside surface and a curved outside surface; see Figure 5a,b.  
The depth of the fins is 116 mm, and the base length is 111 mm; see Figure 6a. Furthermore, the fin's planform area is 9860 mm\({}^{2}\). The initial distances in the transverse direction between the front  
Figure 4: Exemplary proceeding of CT scanning and post-processing: (**a**) A 3-fin NSP surfboard positioned in the CT for scanning; (**b**) post-processed 3D data: surfboard tail cutaway and remaining fins imported in STAR-CCM+.  
Figure 5: (**a**) Cant and Toe-In angle of the surfboard fins. (**b**) The asymmetric and symmetric shapes of the rail fins and the center fin are visible in the bottom view of the surfboard.  
fins are 330 mm and for the rear fins 170 mm; see Figure 6a. The axial distance of the rear fins to the front fins is 150 mm. The entire fin configuration is rotated around an axis to realize the AoA between the fins and the fluid flow, which is located precisely at the center point between the leading edges of the front fins; see Figure 6b.  
Besides the original configuration, ten fin configurations were created by varying the positions of the rear fins within the 4-fin configuration, as displayed in Figure 7a. Therefore, the rear fins were stepwise moved in the axial and transversal direction according to the following constraints:  
1. Both front fins are fixed.
2. Just symmetric fin configurations are realized.
3. The displacement of the rear fins is oriented on the positions of the intersection point board and leading edge.  
Figure 6: (**a**) Dimensions of the initial commercial 4-fin configuration in the axial and transverse direction with fin depth and base. (**b**) The position of the axis of rotation to realize the AoA.  
Figure 7: (**a**) Definition of the transverse and axial direction for the rear fin displacement, (**b**) ten positions of the rear fins for each side (inside fins/outside fins (IF/OF)) marked with red dots. The figure represents the configuration with rear fins positioned at a transversal position of 80 mm and an axial position of 200 mm (T:80 A:200).  
According to these constraints, the ten different configurations are indicated with the red dots in Figure 7b. The commercial CT scanned position of the rear fins corresponds to the configuration 80 mm in the transversal and 150 mm in the axial displacement; see Figure 7a. For a clear definition of the configurations, the following notation is introduced: e.g., T:80 A:150 for the commercial configuration.