## 5 Conclusions  
This study investigated the hydrodynamic performance of the 4-fin configuration with both steady-state and time-dependent simulations. For the first time, a parameter study of the positions of the rear fins within a 4-fin configuration is performed. Additionally, the influence of four different inflow velocities, which represent small and big waves, on the lift and drag forces produced by the fins, is investigated. This study shows an evident and significant influence of the rear fin positioning and the inflow velocity towards the lift and drag performance characteristics. The following points provide a more detailed description of our findings:  
1. The surfer has to apply much more work to perform a turn maneuver with a 4-fin configuration due to the higher lift forces and is losing more velocity during maneuvers because of the higher drag forces compared to a 3-fin configuration.
2. The investigated surfing velocity has nearly no effect on the lift and drag coefficients, but the lift and drag forces increase nonlinearly with increasing velocity.  
At the 4-fin configuration, the front and rear fins of each side act like two large fins when the OFs and RFs are nearly aligned (T:0 A:150 and T:20 A:150) and therefore produce the highest lift forces with a later onset of force fluctuations.  
The maximum of the lift-to-drag ratio increases while shifting the rear fins in the transverse direction toward the longitudinal axis of the surfboard with a fixed axial position.  
Finally, the results indicate a significant impact of the fin positions on the lift and drag forces that significantly influence the speed-up and the maneuverability of the surfboard. Thus, this information is highly relevant for a surfboard design for different surf conditions, including big waves (speed-up) and small waves (maneuverability/tricks).  
The following are available online at [[http://www.mdpi.com/2076-3417/10/3/816/s1](http://www.mdpi.com/2076-3417/10/3/816/s1)]([http://www.mdpi.com/2076-3417/10/3/816/s1](http://www.mdpi.com/2076-3417/10/3/816/s1)), Video SV1: 4-fin_AoA20, Video SV2: 4-fin_AoA25, Video SV3: 4-fin_AoA30, Video SV4: 4-fin_AoA35, Video SV5: 4-fin_AoA40, Video SV6: 4-fin_AoA45.  
Conceptualization, M.D. and S.K. primary M.D.; methodology, S.F., M.D., and S.K.; validation, S,F; formal analysis, S.F.; investigation, M.D., S.K., and S.F.; resources, M.D.; data curation, R.J., R.G., and S.F.; writing--original draft preparation, S.F.; writing--review and editing, M.D., S.K., and T.O.; visualization, S.F.; supervision, M.D. and S.K.; project administration, M.D. and S.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding. None of the authors is affiliated with _FCS_ (Newport Beach, NSW/Australia) nor _ROBERTS Surflowands_ (Ventura, CA, USA).  
The authors acknowledge support from the Central Institute for Scientific Computing (ZISC) and computational resources and support provided by the Erlangen Regional Computing Center (RRZE). Preliminary numeric investigations in fin positioning within a 4-fin configuration were done by [PERSON] in his Master thesis.  
The authors declare no conflict of interest.