# Numerical Investigation of the Hydrodynamic Characteristics of 3-Fin Surfboard Configurations
## 3 Results and Discussion
### Template Comparison  
Figure 9 compares the coefficient data of the baseline template with the two rake templates (a) and the two base templates (b). The small-rake produces a 9.2% increase in the lift at 10\({}^{\circ}\), whilst the large-rake design has only a 6% increase at the same angle. As the AOA reaches the stall point at 20\({}^{\circ}\), the small-rake design reaches a smaller lift peak. Beyond the stall angle (20\({}^{\circ}\)), the large-rake template has a steadier lift drop when compared to the baseline model. The baseline fin stalls at a similar lift peak as the large-rake design; however, at 30\({}^{\circ}\), the \(C_{L}\) drops to a value closer to the small-rake design. This is a loss of around 21.2%, whereas the large-rake only drops by 16.7%. The large-rake design has a higher \(C_{D}\) after the stall (Figure 9a). All the designs have very similar drag until the stall,  
Figure 7: Baseline performance, primary axis: L/D ratio; secondary axis: \(C_{L}\) and \(C_{D}\); X-axis: AOA. where both the small-rake and baseline designs differ from the exponential trend with an increase of 42.7% and 43.8%, respectively, whilst the large-rake design has a greater increase of 52.5% from 20\({}^{\circ}\). Figure 8(b) has a similar trend for the base templates, as was seen in the rake. The small-base is more efficient in the early AOAs, but the large-base has a softer drop in the lift. Despite having similar trends, the base design's performance benefits are smaller. At each AOA, the  
\(C_{L}\) results are smaller than those presented in the rake results, most significantly at the stall point. Although the \(C_{L}\) is smaller, a similar lift loss after stall is evident with a drop of 16.9% for the large-base design. Figure 9(c) reveals a large area of intense turbulence from the trailing edge of the small-rake inside the fin, where, comparably, the large-rake design (Figure 9(d)) has a much smaller and much less intense wake region. The flow reaching the centre fin of the small-rake design would be unpredictable, and this upstream effect is causing the centre fin to exhibit less force as a result. The depth templates exhibited little difference in the \(C_{L}\) and \(C_{D}\) across the designs, as can be seen in Figure 10(a). However, there is a significant impact on the magnitude of the lift force exerted on the fin surface. From the force data given in Figure 10(b), the large-depth design has the highest force output, with a maximum of 662.8 N at 20\({}^{\circ}\), and the small-depth design only has a maximum of 544 N. The baseline has a maximum of 612.9 N.  
The lift and drag results presented suggest the fin parameters investigated are critical factors to consider when fine-tuning surf equipment. It is important to note these simulations simplify the turning of a surfboard in yaw movement, whereas real-world turning involves a complex combination of yaw, pitch, and roll [13]. [PERSON] et al. [17] mentioned higher resultant forces opposing the surfer are an indication of a surfer binding with the wave face and speed increases, or, in surfing terminology, greater \"hold\" and \"drive\". They also note the benefits of lower forces for a surfer as it decreases the amount of power required to perform manoeuvres or improve the \"pivot\" of fins. It is important to recognise the smaller templates for both rake and base length present higher \(C_{L}\) at the angles before stall, whereas the large templates present higher \(C_{L}\) after the stall (Figure 5). The small templates of rake and base length may provide greater speed generation at the  
Figure 9: Lift and drag coefficient versus AOA. (**a**) Baseline vs. large-rake vs. small-rake; (**b**) baseline vs. large-base vs. small-base. lower angles due to higher lift and lower drag. The lower peak lift can also be considered an indication of higher manoeuvrability or \"pivot\" during turns.